Using the probability distribution listed x 0 1 2 3 Px 02 01

Using the probability distribution listed,

x 0 1 2 3

P(x) 0.2 0.1 0.3 0.4

a.) Find the mean, variance, and standard deviation

b.) What is the probability that P(x is at least 1)?

c.) What is the probability that P(x is less than 3)?

a.
mean = 0*0.2 + 1*0.1 + 2*0.3 + 3*0.4
= 1.9

variance = ((0^2)*0.2 + (1^2)*0.1 + (2^2)*0.3 + (3^2)*0.4) - (1.9^2)
= 1.29

standar deviation = sqrt(1.29) = 1.1358

b.
P(X>=1) = 1 - P(0)
= 1 - 0.2
= 0.8

c.
P(X<3) = P(0) + P(1) + P(2)
= 0.2 + 0.1 + 0.3
= 0.6