Question

The probability distribution of X is as follows:

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

Find k and P[X < 2]

Answer 1

As probability distribution of r. v. X is given, `sum"P"("X" = x)` = 1

i.e., P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 1

∴ 0.1 + k + 2k + 2k + k = 1

∴ 6k = 0.9

∴ k = 0.15   .....(i)

∴ P[X < 2] = P(X = 0 or 1)

= P(X = 0) + P(X = 1)

= 0.1 + k

= 0.1 + 0.15     ......[From (i)]

= 0.25