Question
The cumulative distribution function of $X$ is given by the rule$$F(x)= \begin{cases}1 & \text { if } x \geq 2, \\ \frac{1}{4} & \text { if } 1 \leq x<2, \\ 0 & \text { if } x<1 .\end{cases}$$(a) find the corresponding PMF(b) find $P(1<X<2)$.
Step 1
The CDF of a random variable $X$, denoted $F(x)$, is defined as $F(x) = P(X \leq x)$. The given CDF is: $$ F(x)= \begin{cases} 1 & \text{if } x \geq 2, \\ \frac{1}{4} & \text{if } 1 \leq x < 2, \\ 0 & \text{if } x < 1. \end{cases} $$ Show more…
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