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, $\sum\text{P}(\text{X})=1$ ⇒ P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1 ⇒ k + 2k + 3k + 4k =1 ⇒ 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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