Question

The probability distribution of a discrete random variable X is given as under:

X	1	2	4	2A	3A	5A
P(X)	`1/2`	`1/5`	`3/25`	`1/10`	`1/25`	`1/25`

Calculate: The value of A if E(X) = 2.94

Answer 1

We know that: E(X) = `sum_("i" = 1)^"n" "P"_"i""X"_"i"`

∴ E(X) = `1 xx 1/2 + 2 xx 1/5 + 4 xx 3/25 + 2"A" xx 1/10 + 3"A" xx 1/25 + 5"A" xx 1/25`

2.94 = `1/2 + 2/5 + 12/25 + "A"/5 + (3"A")/25 + "A"/5`

⇒ 2.94 = `0.5 + 0.4 + 0.48 + (13"A")/25 = 1.38 + (13'A")/25`

⇒ 2.94 – 1.38 = `(13"A")/25`

⇒ 1.56 = `(13"A")/25`

⇒ A = `(1.56 xx 25)/13` = 0.12 × 25

∴ A = 3