The probability distribution of a random variable X is given below: $$X$$ 4 k $$\frac{30}{7}k$$ $$\f

Question

The probability distribution of a random variable X is given below:

$$X$$	4 k	$$\frac{30}{7}k$$	$$\frac{32}{7}k$$	$$\frac{34}{7}k$$	$$\frac{36}{7}k$$	$$\frac{38}{7}k$$	$$\frac{40}{7}k$$	6 k
$$P(X)$$	$$\frac{2}{15}$$	$$\frac{1}{15}$$	$$\frac{2}{15}$$	$$\frac{1}{5}$$	$$\frac{1}{15}$$	$$\frac{2}{15}$$	$$\frac{1}{5}$$	$$\frac{1}{15}$$

If $E(X) = \frac{263}{15}$, then $P(X < 20)$ is equal to :

Accepted Answer

$E(X) = \sum X_{i}P\left( X_{i} ight) = \frac{526k}{15 	imes 7} = \frac{263}{15} \Rightarrow k = \frac{7}{2}$ X 14 15 16 17 18 19 20 21 $$P(X)$$ $$\frac{2}{15}$$ $$\frac{1}{15}$$ $$\frac{2}{15}$$ $$\frac{1}{5}$$ $$\frac{1}{15}$$ $$\frac{2}{15}$$ $$\frac{1}{5}$$ $$\frac{1}{15}$$ $$P(X < 20) = \sum_{X = 14}^{19}\mspace{2mu} P(X) = \frac{11}{15}$$

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