If the probability distribution of a random variable X is given b… - Vidyadip

Question

If the probability distribution of a random variable $X$ is given below:

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

Write the value of $\text{P}(\text{X}\leq2)$

✓

Answer

We know that the sum of probabilities in a probability distribution is always $1.$
Therefore,
$P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1$
$\Rightarrow c + 2c + 4c + 4c =1$
$\Rightarrow 11c = 1$
$\Rightarrow\text{c}=\frac{1}{11}$
Now,
$\text{P}(\text{X}\leq2)=\text{P}(\text{X}=1)+\text{P}(\text{X})=2=\frac{1}{10}+\frac{2}{10}=\frac{3}{10}$

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