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

Question

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 $\text{P}(\text{X}\geq3).$

✓

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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