Voice calls cost 20 cents each and data calls cost 30 cents each. C is the cost of one telephone call. The probability that a call is a voice call is P[V] = 0.6. The probability of a data ca is P[D] = 0.4. Find the PMF of C What is E[C], the expected value of C?

a) For this case we define the random variable C as "cost of one telephone call". We know that we have two possible values for C 20 or 30 cents, so then we can define the probability mass function like this:

C      |  20    30

P(C)  |  0.6    0.4

b)

We know that :

If we replace we got:

So then the expected value for the random variabe of interest C is 24 cents.

Step-by-step explanation:

Part a

For this case we define the random variable C as "cost of one telephone call". We know that we have two possible values for C 20 or 30 cents, so then we can define the probability mass function like this:

C      |  20    30

P(C)  |  0.6    0.4

Part b

In statistics and probability analysis, the expected value "is calculated by multiplying each of the possible outcomes by the likelihood each outcome will occur and then summing all of those values".

And the definition for the expected value is given by:

We know that :

If we replace we got:

So then the expected value for the random variabe of interest C is 24 cents.