Question:
Let \( X \) be a random variable such that \( X \) and \( -X \) have the same distribution. Let \( Y = X^2 \) be a continuous random variable with the probability density function
\[g(y) = \begin{cases} \frac{e^{-y/2}}{\sqrt{2\pi y}}, & \text{if } y > 0 \\0, & \text{if } y \leq 0 \end{cases}.\]
Then \( E((X - 1)^4) \) is equal to:
Let \( X \) be a random variable such that \( X \) and \( -X \) have the same distribution. Let \( Y = X^2 \) be a continuous random variable with the probability density function
\[g(y) = \begin{cases} \frac{e^{-y/2}}{\sqrt{2\pi y}}, & \text{if } y > 0 \\0, & \text{if } y \leq 0 \end{cases}.\]
Then \( E((X - 1)^4) \) is equal to:
\[g(y) = \begin{cases} \frac{e^{-y/2}}{\sqrt{2\pi y}}, & \text{if } y > 0 \\0, & \text{if } y \leq 0 \end{cases}.\]
Then \( E((X - 1)^4) \) is equal to:
Updated On: Oct 1, 2024
- 9
- 10
- 11
- 12
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The Correct Option is B
Solution and Explanation
The correct option is (B): 10
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