If a random variable x has the probability distribution gathered x 0 1 2 3 4 5 6 7 P(x) 0 …

Question

If a random variable $x$ has the probability distribution

$\begin{gathered} x \quad  0 \quad  1 \quad  2 \quad  3 \quad  4 \quad  5 \quad  6 \quad  7 \ P(x) \quad  0 \quad  2k \quad  k \quad  3k \quad  2{k}^{2} \quad  2k \quad  {k}^{2}+k \quad  7{k}^{2} \end{gathered}$

$P(3<x\le 6)$

Accepted Answer

$\begin{gathered} 2K+K+3K+2{K}^{2}+2K+{K}^{2}+K+7{K}^{2}=1 \ (K+1)(10K-1)=0 \ K=-1K=\frac{1}{10} \ P(3<x\le 6)=\frac{2}{100}+\frac{2}{10}+\frac{1}{100}+\frac{1}{10}=0.33 \end{gathered}$

Solutions · 1