Question

A random variable X has the following probability distribution:

X = x	–1	0	1	2	3	4
P(X = x)	0.25	2k	0.1	k	0.15	2k

Then, the expected value of X is ______.

विकल्प

• 0.5

• 1.5

• 0.7

• 1.3

Answer 1

A random variable X has the following probability distribution:

X = x	–1	0	1	2	3	4
P(X = x)	0.25	2k	0.1	k	0.15	2k

Then, the expected value of X is 1.3.

Explanation:

The sum of all the probabilities in a probability distribution is always unity.

∴ 0.25 + 2k + 0.1 + k + 0.15 + 2k = 1

⇒ 0.5 + 5k = 1

⇒ 5k = 0.5

⇒ k =  0.1

∴ E(X) = `sumx_"i""P"(x_"i")`

= (–1)(0.25) + (0)(2 × 0.1) + (1)(0.1) + (2)(0.1) + (3)(0.15) + 4(2 × 0.1)

= 1.3