Question

A bowl contains four balls numbered 1,2,3,4. If two balls are randomly drawn from the bowl, without replacment , and the random variable X is the sum of the numbers on the two balls drawn.

a) Find the probabiltiy density function.

b) Find P(x>3)

c) Determine the expected value and the standard deviation.

Answer 1

Two balls out of 4 balls can be drawn in 4C2 = 6 ways

The possible cases are (1,2), (1,3), (1,4), (2,3), (2,4), (3,4)

Thus, X can take values 3,4,5,5,6,7

(a) Probability density function

x	3	4	5	6	7
P(x)	1/6	1/6	1/3	1/6	1/6

(b) P(X>3) = P(x=4) + P(x=5) + P(x=6) + P(x=7) = 1/6 + 1/3 + 1/6 + 1/6 = 5/6

(c) Expected value,u = = 3*1/6 + 4*1/6 + 5*1/3 + 6*1/6 +7*1/6 = 5

Variance = =

Thus, standard deviation =?(5/3) = 1.29