Question

The following table gives the probability distribution of a distribute random variable X use the table to find the following probability round solution at 3 festival places

Answer 1

Probability

The right column of the table represents the probability of

x being 0, 1, 2, 3, 4 or 5.

x=0, x=1, x=2, x=3, x=4 or x=5.

P(x = 2)

We have that P(x=2) is the probability of x being 2. The space to the right of x=2:

Then,

P(x = 2) = 0.153

P(x ≤ 1)

We have that x ≤ 1 if x=0 or x=1.

Then, the probability of x ≤ 1 is the addition of the probability of x=0 and x=1:

P(x ≤ 1) = P(x = 0) + P(x = 1)

= 0.305 + 0.185 = 0.490

P(x ≤ 1) = 0.490

Then,

P(x ≤ 1) = 0.490

P(x ≥ 4)

We have that x ≥ 4 if x=4 or x=5.

Then, the probability of x ≥ 4 is the addition of the probability of x=4 and x=5:

P(x ≥ 4) = P(x = 4) + P(x = 5)

= 0.136 + 0.085

= 0.221

Then,

P(x ≥ 4) = 0.221

P(1 ≤ x ≤ 3)

We have that 1 ≤ x ≤ 3 if x=1, x=2 or x=3.

Then, the probability of1 ≤ x ≤ 3 is the addition of the probability of x=1, x=2 and x=3:

P(1 ≤ x ≤ 3) = P(x = 1) + P(x = 2) + P(x = 3)

= 0.185 + 0.153 + 0.136

= 0.474

Then,

P(1 ≤ x ≤ 3) = 0.474

Type of distribution

We observe that the probability decreases when x increase.

Then, this can be a geometric distribution