A random variable has the following probability distribution: X = X_i 1 2 3 4 P(X = X_i) k 2k 3k 4k Write the value of P(X 3).

Here, X = X_i 1 2 3 4 P(X = X_i) k 2k 3k 4k Since, (X)=1 P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1 k + 2k + 3k + 4k =1 10k = 1 =1 10 P(X 3)= P(X = 3) + P(X = 4) = 3k + 4k = 7k =1 10 P(X 3)=7 10

A random variable has the following probability distribution: X =…

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A random variable has the following probability distribution:

$X = X_i$	$1$	$2$	$3$	$4$
$P(X = X_i)$	$k$	$2k$	$3k$	$4k$

Write the value of $\text{P}(\text{X}\geq3).$

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Answer

Here,

$X = X_i$	$1$	$2$	$3$	$4$
$P(X = X_i)$	$k$	$2k$	$3k$	$4k$

Since, $\sum\text{P}(\text{X})=1$
$\Rightarrow P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1$
$\Rightarrow k + 2k + 3k + 4k =1$
$\Rightarrow 10k = 1$
$\Rightarrow\text{k}=\frac{1}{10}$
$\text{P}(\text{X}\geq3)= P(X = 3) + P(X = 4)$
$= 3k + 4k$
$= 7k =\frac{1}{10}$
$\text{P}(\text{X}\geq3)=\frac{7}{10}$

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