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:

1. k
2. P[X < 2]
3. P[X ≥ 3]
4. P[1 ≤ X < 4]
5. P(2)

The probability distribution of X is as follows:

x	0	1	2	3	4
P[X = x]	0.1	K	2K	2K	K

Find:

1. K
2. P(X < 2)
3. P(X ≥ 3)

The probability distribution of X is as follows:

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

Find:

1. k
2. P(X < 2)

Answer 1

a. The table gives a probability distribution and therefore P[X = 0] + P[X = 1] + P[X = 2] + P[X = 3] + P[X = 4] = 1

i.e., 0.1 + k + 2k + 2k + k = 1

i.e., 6k = 0.9

∴ k = 0.15

k = 0.15

b. P[X < 2] = P[X = 0] + P[X = 1]

= 0.1 + k

= 0.1 + 0.15

= 0.25

c. P[X ≥ 3] = P[X = 3] + P[X = 4]

= 2k + k

= 3k

= 3(0.15)

= 0.45

d. P[1 ≤ X < 4] = P[X = 1] + P[X = 2] + P[X = 3]

= k + 2k + 2k

= 5k

= 5(0.15)

= 0.75

e. P(2) = P[X ≤ 2] = P[X = 0] + P[X = 1] + P[X = 2]

= 0.1 + k + 2k

= 0.1 + 3k

= 0.1 + 0.45

= 0.55