X is a uniformly distributed random variable that takes values between 0 and 1. The value of $E (X^{4})$ will be ____.
0.2

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Solution

The correct option is A 0.2
$fx (X) = (\begin{matrix} 1 & 0 < x < 1 0 & Otherwise \end{matrix}$

$E (X^{4}) = \int_{- \infty}^{\infty} x^{4} . f_{x} (X) d x$

$= \int_{0}^{1} x^{4} . 1 d x = \begin{matrix} \frac{x^{5}}{5} \end{matrix} {∣ ∣}_{0}^{1} = \frac{1}{5} = 0.2$

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X is a uniformly distributed random variable that takes values between 0 and 1. The value of E(X4) will be ____.0.2

The correct option is A 0.2 fx(X)=(10<x<10Otherwise E(X4)=∫∞−∞x4.fx(X)dx =∫10x4.1 dx=x55∣∣10=15=0.2

X is a uniformly distributed random variable that takes values between 0 and 1. The value of $E (X^{4})$ will be ____.
0.2

The correct option is A 0.2
$fx (X) = (\begin{matrix} 1 & 0 < x < 1 0 & Otherwise \end{matrix}$

$E (X^{4}) = \int_{- \infty}^{\infty} x^{4} . f_{x} (X) d x$

$= \int_{0}^{1} x^{4} . 1 d x = \begin{matrix} \frac{x^{5}}{5} \end{matrix} {∣ ∣}_{0}^{1} = \frac{1}{5} = 0.2$