Question

B1) The random variable Krepresents the number of typing errors per page in a student' dissertation, with the following probability distribution: [SKI: 5 Marks] 00.05 0.30 2 0.40 3 0.15 4 0.10 1) Find the expected number of errors per page. 2) Find the variance and standard deviation of the random variable. 3) Find the following probability: P(X23) (2 Marks) (2 Marks) (1 Marks)

Answer 1

1)

Expected Number of Errors E(x) = sum of x*f(x)

E(x) = 0*0.05+1*0.30+2*0.40+3*0.15+4*0.10

E(x) = 1.95

2)

Variance V(x) = Sum of x^2*f(x)

V(x) = 0^2*0.05+1^2*0.30+2^2*0.40+3^2*0.15+4^2*0.10

V(x) = 4.85

SD = (V(x)^(1/2)

SD = (4.85)^(1/2)

SD = 2.20

3)

P(X>=3) = 1 - P(X<3)

P(X>=3) = 1 - P(X =0) - P(X =1) - P(X =2)

P(X>=3) = 1 - 0.05 - 0.30 - 0.40

P(X>=3) = 0.25