The probability density function (pdf) of continuous random variable X is as follows: x<0 0

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The probability density function (pdf) of continuous random variable X is as follows:

\[ 
f(x) = 
\begin{cases} 
0 & x \leq 0 \\
x^2 & 0 \leq x \leq 1 \\
\frac{4x}{9} & 1 \leq x \leq 2 \\
0 & x \geq 2 \\
\end{cases} 
\]

Tasks:
a. Determine the cumulative density function (cdf) of the random variable X.

b. Compute the probability that X is less than or equal to 0.5.

c. Compute the probability that X is greater than or equal to 1.5.

d. Compute the probability that X is between 0.5 and 1.5.
Transcribed Image Text:The probability density function (pdf) of continuous random variable X is as follows: \[ f(x) = \begin{cases} 0 & x \leq 0 \\ x^2 & 0 \leq x \leq 1 \\ \frac{4x}{9} & 1 \leq x \leq 2 \\ 0 & x \geq 2 \\ \end{cases} \] Tasks: a. Determine the cumulative density function (cdf) of the random variable X. b. Compute the probability that X is less than or equal to 0.5. c. Compute the probability that X is greater than or equal to 1.5. d. Compute the probability that X is between 0.5 and 1.5.
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