Question:medium
If \( X \) is a random variable with the probability mass function (p.m.f.) as follows:
\[
P(X = x) = \begin{cases}
\frac{5}{16}, & x = 0, \\
\frac{kx}{48}, & x = 1, \\
\frac{1}{4}, & x = 2, \\
\frac{1}{4}, & x = 3,
\end{cases}
\]
then find \( E(X) \):
If \( X \) is a random variable with the probability mass function (p.m.f.) as follows:
\[
P(X = x) = \begin{cases}
\frac{5}{16}, & x = 0, \\
\frac{kx}{48}, & x = 1, \\
\frac{1}{4}, & x = 2, \\
\frac{1}{4}, & x = 3,
\end{cases}
\]
then find \( E(X) \):
Show Hint
To calculate the expected value \( E(X) \), ensure that the total probability sums to 1 and substitute each \( x \cdot P(X = x) \) term carefully into the summation formula.
Updated On: Nov 26, 2025
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