Consider the following probability mass function p-m-f- of a random variable X-px- q-qif X-01-qif X-10otherwiseIf q - 0-4- the variance of X is -

nbsp; x 0 1 p(x) q 1 q E(x)=∑_ix_ip_i=0× q+1× (1 q) = 1 q = 0.6 ...

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Mathematical Expectation

Consider the ...

Question

Consider the following probability mass function (p.m.f.) of a random variable X.

$p ⎛ ⎜ ⎝ x, q ⎞ ⎟ ⎠ = ⎛ ⎜ ⎝ \begin{matrix} q & if X = 0 1 - q & if X = 1 0 & otherwise \end{matrix}$

If q = 0.4, the variance of X is .

0.24

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x

P (x) = ⎧ ⎪ ⎨ ⎪ ⎩ \begin{matrix} (\frac{4}{x}) {(\frac{5}{9})}^{x} {(\frac{4}{x})}^{4 - x}, x = 0, 1, 2, 3, 4 0, otherwise \end{matrix}

E (x)

(x)

x

X = x_{1} : - 2 - 10123

p (X = x_{1}) : 0.1 k 0.2 2 k 0.3 k

x

X

$X$	$- 2$	$3$	$1$
$P (X = x)$	$\frac{λ}{6}$	$\frac{λ}{4}$	$\frac{λ}{12}$

λ

X

$X = x$	$0$	$1$	$2$	$3$
$P (X = x)$	$k$	$3 k$	$3 k$	$k$

k

X

P (X = x) = 0.1, 0.1, 0.1, 0.3, 0.4

(X = x) = 4, 3, 2, 1, 0

X

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