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,
$P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1$
$⇒ c + 2c + 4c + 4c =1$
$⇒ 11c = 1$
$\Rightarrow\text{c}=\frac{1}{11}$
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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