Chapter 9 Random Variables And Distributions Statistics 12th Class Punjab MCQ Tests
12th Class Statistics Chapter 9 MCQ Tests
Chapter 9 of 12th Class Statistics has 30 questions. If you take an online MCQ test, the system will randomly choose the questions. If you want to take the quiz by chapter then click the start test button.
Total Questions: 30
Total Marks: 30
Time: 30 Mins
Total Questions: 30
Total Marks: 30
Time: 30 Mins
30Min : 00 Sec Remaining
Question # 1
An insurance policy pays a total medical benefit consisting of a part paid to the surgeon, X, and a part paid to the hospital, Y , so that the total benefit is X+Y. Suppose that Var(X) = 5, 000, Var(Y) = 10, 000, and Var(X + Y) = 17, 000. If X is increased by a flat amount of 100, and Y is increased by 10%, what is the variance of the total benefit after these increases?
Question # 2
If P(X = 1) = 0.1, P(X = 2) = 0.2, P(X = 3) = 0.3, P(X = 4) = 0.4 and Y=9X + 14, what is the variance of Y?
Question # 3
Consider the gambling game in which the casino chooses to lower each payout by $1.00, then double each prize. If the new variance is 15.84 then what is the original variance ?
Question # 4
The number of questions that you answer correctly on this practice quiz is an example of:
Question # 5
Ali is analyzing his basketball throws. The following table shows a probability model for the results from his next two free throws.
Is this valid probability distribution?
Question # 6
If X and Y are two independent variables then E(XY) will be:
Question # 7
Let X be the profit that a person makes in a business. He may earn Rs. 2800 with a probability 0.5, he may lose Rs 5500 with probability 0.3 and he may neither earn nor lose with a probability 0.2. Calculate E(X).
Question # 8
Let X and Y be discrete random variables with joint mass function defined by f(x, y) = 1/4, and (x, y) ϵ {(0, 0),(1, 1),(1, -1),(2, 0)} , find Var(X - 2Y).
Question # 9
If we have f(x) = 2x, 0 ≤ x ≥ 1, then f(x) is said to be:
Question # 10
Beth earns $25.00 an hour for tutoring but spends $20.00 an hour for piano lessons. She saves the difference between her earnings for tutoring and the cost of the piano lessons. The numbers of hours she spends on each activity in one week vary independently according to the probability distributions shown below. The standard deviation of hours Beth spends in one week on piano lessons and tutoring is 0.831 and 1.11 hours. Likewise, the expected number of hours Beth spends tutoring is 2.6 with the standard deviation of 1.11 hours. What is the standard deviation of her weekly savings is if she spends $20 for each hour of piano lessons, Beth earns $25 for each hour of tutoring.
Question # 11
The share of a company has values 10, 20 and 25 of return of investment along with their respective probabilities 0.45, 0.35 and 0.20. What is the expected value of return on investment?
Question # 12
When four coins are tossed, what are the values of the random variable (number of heads)?
Question # 13
Suppose that the cost of maintaining a car is given by a random variable, X, with mean 200 and variance 260. If a tax of 20% is introduced on all items associated with the maintenance of the car, what will the variance of the cost of maintaining a car be?
Question # 14
The profit for a new product is given by Z=3X−Y−5, where X and Y are independent random variables with Var(X) = 1 and Var(Y) = 2. What is the variance of Z?
Question # 15
Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0.29, 0.40, 0.35. profit per unit is $0.50 then what are the expected profits for three days?
Question # 16
If three balls are selected from a box containing two black balls and four red balls, then what is the minimum value of random variable X if X= number of red balls?
Question # 17
Consider the following probability distribution:
Question # 18
Class of variable which can accept any value within upper and lower limit is classified as:
Question # 19
Find the constant c such that the function is a density function.
Question # 20
A spinner that could take on any value 0º ≤ x ≤ 360º. Density function:
Find its CDF
Question # 21
A box contain two defective and five non defective mobiles, if three mobiles are selected at random then how many possible values of random variable i.e. number of defective mobiles are there?
Question # 22
A House of Gambling has a roulette wheel containing 38 numbers: zero (0), double zero (00), and the numbers 1, 2, 3, ..., 36. Let X denote the number on which the ball lands and u(X) denote the amount of money paid to the gambler, such that
Question # 23
You are a space alien. You visit planet Earth and abduct 97 chickens, 47 cows, and 77 humans. Then, you randomly select one Earth creature from your sample to experiment on. Each creature has an equal probability of getting selected. Create a probability model.
Question # 24
What is Var(X) when X is outcome of one fair die?
Question # 25
Question # 26
Probability distribution of discrete random variable is classified as:
Question # 27
A service organization in a large town organizes a raffle each month. One thousand raffle tickets are sold for $1 each. Each has an equal chance of winning. First prize is $300, second prize is $200, and third prize is $100. Let X denote the net gain from the purchase of one ticket. Construct the probability distribution of X.
Question # 28
Life expectancy of a certain bacteria having the density function
Find the probability of bacteria living from 2 to 5 days.
Question # 29
If probability density function of a random variable X is given to be
Question # 30
Suppose we toss a penny three times. Let X1 denote the number of heads that we get in the three tosses. And, suppose we toss a second penny two times. Let X2 denote the number of heads we get in those two tosses. Let Y=X1+X2 then Y denotes the number of heads in five tosses. Find the expected value of Y.
Total Questions
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Question # 1
An insurance policy pays a total medical benefit consisting of a part paid to the surgeon, X, and a part paid to the hospital, Y , so that the total benefit is X+Y. Suppose that Var(X) = 5, 000, Var(Y) = 10, 000, and Var(X + Y) = 17, 000. If X is increased by a flat amount of 100, and Y is increased by 10%, what is the variance of the total benefit after these increases?
Question # 2
If P(X = 1) = 0.1, P(X = 2) = 0.2, P(X = 3) = 0.3, P(X = 4) = 0.4 and Y=9X + 14, what is the variance of Y?
Question # 3
Consider the gambling game in which the casino chooses to lower each payout by $1.00, then double each prize. If the new variance is 15.84 then what is the original variance ?
Question # 4
The number of questions that you answer correctly on this practice quiz is an example of:
Question # 5
Ali is analyzing his basketball throws. The following table shows a probability model for the results from his next two free throws.
Is this valid probability distribution?
Question # 6
If X and Y are two independent variables then E(XY) will be:
Question # 7
Let X be the profit that a person makes in a business. He may earn Rs. 2800 with a probability 0.5, he may lose Rs 5500 with probability 0.3 and he may neither earn nor lose with a probability 0.2. Calculate E(X).
Question # 8
Let X and Y be discrete random variables with joint mass function defined by f(x, y) = 1/4, and (x, y) ϵ {(0, 0),(1, 1),(1, -1),(2, 0)} , find Var(X - 2Y).
Question # 9
If we have f(x) = 2x, 0 ≤ x ≥ 1, then f(x) is said to be:
Question # 10
Beth earns $25.00 an hour for tutoring but spends $20.00 an hour for piano lessons. She saves the difference between her earnings for tutoring and the cost of the piano lessons. The numbers of hours she spends on each activity in one week vary independently according to the probability distributions shown below. The standard deviation of hours Beth spends in one week on piano lessons and tutoring is 0.831 and 1.11 hours. Likewise, the expected number of hours Beth spends tutoring is 2.6 with the standard deviation of 1.11 hours. What is the standard deviation of her weekly savings is if she spends $20 for each hour of piano lessons, Beth earns $25 for each hour of tutoring.
Question # 11
The share of a company has values 10, 20 and 25 of return of investment along with their respective probabilities 0.45, 0.35 and 0.20. What is the expected value of return on investment?
Question # 12
When four coins are tossed, what are the values of the random variable (number of heads)?
Question # 13
Suppose that the cost of maintaining a car is given by a random variable, X, with mean 200 and variance 260. If a tax of 20% is introduced on all items associated with the maintenance of the car, what will the variance of the cost of maintaining a car be?
Question # 14
The profit for a new product is given by Z=3X−Y−5, where X and Y are independent random variables with Var(X) = 1 and Var(Y) = 2. What is the variance of Z?
Question # 15
Demand of products per day for three days are 21, 19, 22 units and their respective probabilities are 0.29, 0.40, 0.35. profit per unit is $0.50 then what are the expected profits for three days?
Question # 16
If three balls are selected from a box containing two black balls and four red balls, then what is the minimum value of random variable X if X= number of red balls?
Question # 17
Consider the following probability distribution:
Question # 18
Class of variable which can accept any value within upper and lower limit is classified as:
Question # 19
Find the constant c such that the function is a density function.
Question # 20
A spinner that could take on any value 0º ≤ x ≤ 360º. Density function:
Find its CDF
Question # 21
A box contain two defective and five non defective mobiles, if three mobiles are selected at random then how many possible values of random variable i.e. number of defective mobiles are there?
Question # 22
A House of Gambling has a roulette wheel containing 38 numbers: zero (0), double zero (00), and the numbers 1, 2, 3, ..., 36. Let X denote the number on which the ball lands and u(X) denote the amount of money paid to the gambler, such that
Question # 23
You are a space alien. You visit planet Earth and abduct 97 chickens, 47 cows, and 77 humans. Then, you randomly select one Earth creature from your sample to experiment on. Each creature has an equal probability of getting selected. Create a probability model.
Question # 24
What is Var(X) when X is outcome of one fair die?
Question # 25
Question # 26
Probability distribution of discrete random variable is classified as:
Question # 27
A service organization in a large town organizes a raffle each month. One thousand raffle tickets are sold for $1 each. Each has an equal chance of winning. First prize is $300, second prize is $200, and third prize is $100. Let X denote the net gain from the purchase of one ticket. Construct the probability distribution of X.
Question # 28
Life expectancy of a certain bacteria having the density function
Find the probability of bacteria living from 2 to 5 days.
Question # 29
If probability density function of a random variable X is given to be
Question # 30
Suppose we toss a penny three times. Let X1 denote the number of heads that we get in the three tosses. And, suppose we toss a second penny two times. Let X2 denote the number of heads we get in those two tosses. Let Y=X1+X2 then Y denotes the number of heads in five tosses. Find the expected value of Y.
Total Questions
123456789101112131415161718192021222324252627282930
Statistics MCQ Test by Topics
- +9.1 Random Variables
- +9.2 Discrete Probability Distribution
- +9.3 Continuous Probability Distribution
- +9.4 The Expectation of Random Variable
- +9.5 Properties of Variances
- +9.6 Sum or Differences of Variances of Random Variables
Statistics
- Representation and Exploration of Data
- Measure of Central Tendency or Averages
- Measures of Dispersion
- Index Numbers
- Regression and Correlation Analysis
- Analysis of Time Series
- Set Theory
- Introduction to Probability
- Random Variables and Distributions
- Binomial and Hypergeometric Distributions
- The Normal Distribution
- Sampling and Sampling Distributions
- Statistical Inference:Estimation
- Statistical Inference:Hypothesis Testing
- Association of Attributes
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Updated on: 02-09-2026
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