(1 point) An insurance company offers its policyholders a number of different premium payment options. For a randomly selected policyholder, let X be the number of months between successive payments. The CDF(cumulative distribution function) of X: F(x)=0, if x < 1,
F(x)=0.4, if 1 <_ x < 3,
F(x)=0.6, if 3 <_ x < 5,
F(x)=0.8, if 5 <_ x < 7,
F(x)=1.0, if x >_ 7.
(a) What is the probability mass function of X?
(b) Compute P(4 < X <_ 7) of X is .

a)

X    |  1        3      5       7

f(X) | 0.4   0.2   0.2    0.2

b)

Step-by-step explanation:

For this case we have defined the cumulative distribution function like this:

And we know that the general definition for the distribution function is given by:

Where f represent the density function.

Part a

For this case we need to find the density function, so we can find the values for the density for each value of X = 1,2,3,4,5,6,7,... since X is a discrete random variable.

And for any value higher than 7 we have that:

So then we have our density function defined like this:

X    |  1        3      5       7

f(X) | 0.4   0.2   0.2    0.2

Part b

For this case we want to find this probability

And since the random variable is discrete we can write this like that:

there are 25 people coming to the party

step-by-step explanation:

the text says that there will be 22 children at this party, 1 teacher, and 2 parents. so if you add them all together (22+1+2) it will equal 25. (=25)