CUET-UG SERIES

Mathematics

Probability And Statistics

4 previous year questions.

Volume: 4 Ques

Yield: Medium

High-Yield Trend

4

2025

Chapter Questions
4 MCQs

01

PYQ 2025

easy

mathematics ID: cuet-ug-

The probability distribution of the random variable X is given by X 0123 P(X) 0.2 k 2k 2k Find the variance of the random variable .

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3

1

4

Official Solution

Correct Option: (1)

Step 1: Understanding the Concept: This question tests the knowledge of finding the variance of a discrete random variable given its probability distribution. First, we must find the value of the unknown 'k' using the property that the sum of all probabilities in a distribution is 1. Then, we calculate the mean (Expected Value,) and the expectation of the square of the variable (). Finally, we use the variance formula. Step 2: Key Formula or Approach: 1. Sum of probabilities: . 2. Mean (Expected Value): . 3. Expectation of : . 4. Variance: . Step 3: Detailed Explanation: Find k: The sum of all probabilities must be 1. Now we can complete the probability distribution table: X 0123 P(X) 0.2 0.16 0.32 0.32 Calculate Mean : Calculate : Calculate Variance : Convert to Fraction: Now, let's check the options. Option (A): . Let's calculate this value: . This matches our calculated variance. Step 4: Final Answer: The variance of the random variable is 1.2224, which is equal to .

02

PYQ 2025

medium

mathematics ID: cuet-ug-

What is the mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on 1 face?

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2

2

4

3

1

4

8

03

PYQ 2025

medium

mathematics ID: cuet-ug-

What is the mean of the numbers obtained on throwing a die having written 1 on three faces, 2 on two faces and 5 on 1 face?

1

2

2

4

3

1

4

8

04

PYQ 2025

medium

mathematics ID: cuet-ug-

The probability distribution of the random variable X is given by \begin{tabular}{|l|l|l|l|l|} \hline X & 0 & 1 & 2 & 3 \\ \hline P(X) & 0.2 & k & 2k & 2k \\ \hline \end{tabular} The variance of the random variable X is

1

2

3

1

4

Official Solution

Correct Option: (1)

Step 1: Understanding the Concept: This question tests the knowledge of finding the variance of a discrete random variable given its probability distribution. First, we must find the value of the unknown 'k' using the property that the sum of all probabilities in a distribution is 1. Then, we calculate the mean (Expected Value,) and the expectation of the square of the variable (). Finally, we use the variance formula. Step 2: Key Formula or Approach: 1. Sum of probabilities: . 2. Mean (Expected Value): . 3. Expectation of : . 4. Variance: . Step 3: Detailed Explanation: Find k: The sum of all probabilities must be 1. Now we can complete the probability distribution table: X 0123 P(X) 0.2 0.16 0.32 0.32 Calculate Mean : Calculate : Calculate Variance : Convert to Fraction: Now, let's check the options. Option (A): . Let's calculate this value: . This matches our calculated variance. Step 4: Final Answer: The variance of the random variable is 1.2224, which is equal to .