Question

I. A random variable X has pdf: X 0 1 2 f(x) 3 1/8 3/8 3/8 1/8 (a) Find the cumulative distribution function F(x) (b) Graph this distribution function. II. If the probability of a defective bolt is 0.1, find:  (a) the mean, for the number of defective bolts in a total of 400 bolts. (b) the standard deviation, for the number of defective bolts in a total of 400 bolts. 

Answer 1

I.

a)

$x=0$ : cum. freq.=1/8

$x=1$ : cum. freq.=1/8+3/8=1/2

$x=2$ : cum. freq.=1/8+3/8+3/8=7/8

$x=3$ : cum. freq.=1/8+3/8+3/8+1/8=1

b)

II.

a)

$E(X)=0.1\cdot400=40$

b)

$\sigma=\sqrt{npq}=\sqrt{40(1-0.1)}=6$