A chemical supply company ships a certain solvent in 10-gallon drums. Let X represent the number of drums ordered by a randomly chosen customer. Assume X has the following probability mass function:

x 0 1 2 3 4
p(x) 0.4 0.2 0.2 0.1 0.1

(a) Find the mean number of drums ordered.
(b) Find the variance of the number of drums ordered.
(c) Find the standard deviation of the number of drums ordered.

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khansawaqar7 khansawaqar7 · Answer 1 · 2020-02-26T04:58:50+01:00

Answer:

a) 1.3

b) 1.81

c) 1.345

Step-by-step explanation:

a)

Mean number of drums= E(x)= sum[x*p(x)]

x p(x) x*p(x)

0 0.4 0

1 0.2 0.2

2 0.2 0.4

3 0.1 0.3

4 0.1 0.4

Mean number of drums=0+0.2+0.4+0.3+0.4

Mean number of drums=1.3

b)

Variance of the number of drums= E(x²)-[E(x)]²= sum[x²*p(x)]-[sum[x*p(x)]]²

x p(x) x*p(x) x² x²*p(x)

0 0.4 0 0 0

1 0.2 0.2 1 0.2

2 0.2 0.4 4 0.8

3 0.1 0.3 9 0.9

4 0.1 0.4 16 1.6

E(x²)=sum[x²*p(x)]=0+0.2+0.8+0.9+1.6=3.5

Variance of the number of drums=3.5-[1.3]²

Variance of the number of drums=3.5-1.69

Variance of the number of drums=1.81

c)

Standard deviation of the number of drums=√Variance of the number of drums

Standard deviation of the number of drums=√1.81

Standard deviation of the number of drums=1.345