# Question Q-5: [7+5+8 Marks] Consider the random variable $$\mathrm{X}$$ that has the cumulative distribution function $$\mathrm{F}(\mathrm{x})=$$ $\begin{array}{ll} 0 & \mathrm{x}<0 \\ \frac{x^{2}}{4} & 0 \leq \mathrm{x}<2 \\ 1 & \mathrm{x} \geq 2 \end{array}$ a) Find the probability density function. b) Find $$\mathrm{P}(\mathrm{X}<1)$$ c) Find the mean of Q-5: [7+5+8 Marks] Consider the random variable X that has the cumulative distribution function F(x)= 04x2​1​x<00≤x<2x≥2​ a) Find the probability density function. b) Find P(X<1) c) Find the mean of the random variable X.

2ZFOWU The Asker · Probability and Statistics

Transcribed Image Text: Q-5: [7+5+8 Marks] Consider the random variable X that has the cumulative distribution function F(x)= 04x2​1​x<00≤x<2x≥2​ a) Find the probability density function. b) Find P(X<1) c) Find the mean of the random variable X.
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Transcribed Image Text: Q-5: [7+5+8 Marks] Consider the random variable X that has the cumulative distribution function F(x)= 04x2​1​x<00≤x<2x≥2​ a) Find the probability density function. b) Find P(X<1) c) Find the mean of the random variable X.