The Deans Office keeps track of student complaints received

The Dean\'s Office keeps track of student complaints received each week. The probability distribution for complaints can be represented as a table as shown below. The random variable xi represents the number of complaints, and p(xi) is the probability of receiving xi complaints.

1. What is the probability that they receive less than 3 complaints in a week?

2. What is the average number of complaints received per week?

3. If Xhas the following probability distribution

x 1 2 3 4

p(x) .2 .3 .3 .2

Computed the expected value of X.

4. Assume X has the following probability distribution:

x 1 2 3 4

p(x) .2 .3 .3 .2

Compute the standard deviation of X.

Solution

1)

P(X<3) = P(X=0) + P(X=1) + P(X=2)

= 0.1 + 0.15 + 0.18 = 0.43

2)

average number of complaints = x * P(X)

= 0 * 0.1 + 1 * 0.15 + 2 * 0.18 + 3 * 0.2 + 4 * 0.2 + 5 * 0.1 + 6 * 0.07

= 2.82

3)

expected value of x = x * P(X)

= 1 * 0.2 + 2 * 0.3 + 3 * 0.3 + 4 * 0.2

= 2.5

4)

E(X^2) = x^2 * P(x)

= 1 * 0.2 + 4 * 0.3 + 9 * 0.3 + 16 * 0.2

= 7.3

variance = E(x^2) - E(x)^2

= 7.3 - 2.5^2

= 1.05

standard deviation = sqrt(variance)

= 1.025