Question:
If a random variable \(X\) has mean 3 and standard deviation 5, then the variance of \(Y = 2X - 5\) is:
If a random variable \(X\) has mean 3 and standard deviation 5, then the variance of \(Y = 2X - 5\) is:
Show Hint
Use \(\text{Var}(aX+b) = a^2\text{Var}(X)\); the constant \(-5\) does not change the variance.
Updated On: Jul 4, 2026
- 45
- 100
- 10
- 40
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: The standard deviation of \(X\) is 5, so the variance of \(X\) is \[\text{Var}(X) = 5^2 = 25\]
Step 2: Use the property that for constants \(a\) and \(b\), \[\text{Var}(aX + b) = a^2 \, \text{Var}(X)\] Here \(Y = 2X - 5\), so \(a = 2\) and \(b = -5\). The additive constant \(b\) does not affect variance.
Step 3: Substitute the values: \[\text{Var}(Y) = 2^2 \times 25 = 4 \times 25 = 100\]
So the variance of \(Y\) is 100, which is option (B). (Note: the mean of \(X\), which is 3, is not needed for this calculation since it only affects the mean of \(Y\), not its variance.)
Was this answer helpful?
0
0
Top CPET Statistics Questions
- The statements below relate to Bayes theorem in probability:
(i) Bayes theorem gives a formula to compute conditional probability.
(ii) The posterior probability computed by Bayes theorem supersedes the prior probability.
(iii) Bayes theorem can be used to compute probabilities of past events on the basis of the occurrences of subsequent events.
Identify the correct answer: - If \(P(A) = 0.25\), \(P(B|A) = 0.5\), \(P(B|\bar{A}) = 0.75\) then \(P(A|B)\) is ______.
- Three functions \(F_1(x)\), \(F_2(x)\) and \(F_3(x)\) are defined below:
(i) \(F_1(x) = 0\), for all \(x \in (-\infty, +\infty)\)
(ii) \(F_2(x) = 1\), for all \(x \in (-\infty, +\infty)\)
(iii) \(F_3(x) = 0\), for all \(x \le 0\) and \(F_3(x) = 1\), for all \(x > 0\)
Which of the above functions is a distribution function of a random variable? - Three numbers \(X\), \(Y\), \(Z\) are randomly drawn from the set \(\{1, 2, 3, 4\}\). \(E(XYZ)\) is equal to:
- A cold drinks bottling plant produces 1% defective bottles. The probability that there will be no defective in a lot of 100 bottles is nearest to:
View More Questions
Top CPET Expectation and Variance Questions
Top CPET Questions
- Which of the following is a key reason for choosing DRAM over SRAM for main memory?
- Which of the following components in an FPGA is responsible for implementing combinational and sequential logic?
- What is the main purpose of declaring a base class as virtual in multiple inheritance?
- What happens if a class contains at least one pure virtual function?
- What happens if a derived class defines a function with the same name as a base class function, but with a different parameter list?
View More Questions