First slide

Random variable and probability distribution

Question

Two cards are drawn successively with replacement from a pack of cards. Taking the random variable X = the number of kings, the variance of X is

Easy

A

2/13
B

9/13
C

24/169
D

1/13

Solution

$X = x_{i}$ 0 1 2
$P (X = x_{i})$ $\frac{144}{169}$ $\frac{24}{169}$ $\frac{1}{169}$

$μ = Σ x_{i} P (X = x_{i})$
$= 0 (\frac{144}{169}) + 1 (\frac{24}{169}) + 2 (\frac{1}{169}) = \frac{26}{169} = \frac{2}{13}$

$σ^{2} = Σ x_{i}^{2} P (X = x_{i}) - μ^{2}$
$= 0 (\frac{144}{169}) + 1 (\frac{24}{169}) + 4 (\frac{1}{169}) - \frac{4}{169} = \frac{24}{169}$

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