Find k such that the function Px- k- 4- x - x-0-1-2-3-4-k-0 0- otherwise is a probability mass function-

As sum of all probabilities =1 ⇒ R(^4C_0+^4C_1+^4C_2+^4C_3+^4C_4)=1 =R(1+4+6+4+1)=1 ⇒ R(16)=1 ⇒ R=116 . ...

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Probability Distribution

Find k such...

Question

Find $k$ such that the function
$P (x) = ⎧ ⎨ ⎩ \begin{matrix} k (\begin{matrix} 4 x \end{matrix}); x = 0, 1, 2, 3, 4, k > 0 0; o t h e r w i s e \end{matrix}$ is a probability mass function.

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f (x) = (\begin{matrix} {ke}^{n} e^{- x}; & x \geq 0 0; & otherwise \end{matrix}

C

P (X = k) = C k^{2}

X

0, 1, 2, 3, 4

X

$x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$
$P (X = x)$	$k$	$3 k$	$5 k$	$7 k$	$9 k$	$11 k$	$13 k$

k

P (X < 4), P (X

\geq

5)

P (3 < X

\leq

6)

x

P (X

\leq

x) >

\frac{1}{2}

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)

p (x) = K e^{- α | x |}, x ϵ (- \infty, \infty),

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