An insurance company offers its policyholders a number of different payment options. For a randomly selected policyholder, let X = the number of months between successive payments. The cdf of X is as follows: $$F ( x ) = \left\{ \begin{array} { l l } 0 & x

Question

An insurance company offers its policyholders a number of different payment options. For a randomly selected policyholder, let X = the number of months between successive payments. The cdf of X is as follows: $$F ( x ) = \left\{ \begin{array} { l l } 
0 & x < 1 \
30 & 1 \leq x < 3 \
40 & 3 \leq x < 4 \
.45 & 4 \leq x < 6 \
.60 & 6 \leq x < 12 \
1 & 12 \leq x
\end{array} \right.$$ 
a. What is the pmf of X?
b. Using just the cdf, compute $P ( 3 \leq X \leq 6 ) \text { and } P ( X \geq 4 )$ 
c. Using just the pmf, compute P(X>6).

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The Answer of An insurance company offers its policyholders a number of different payment options. For a randomly selected policyholder, let X = the number of months between successive payments. The cdf of X is as follows: $$F ( x ) = \left\{ \begin{array} { l l } 
0 & x < 1 \
30 & 1 \leq x < 3 \
40 & 3 \leq x < 4 \
.45 & 4 \leq x < 6 \
.60 & 6 \leq x < 12 \
1 & 12 \leq x
\end{array} \right.$$ 
a. What is the pmf of X?
b. Using just the cdf, compute $P ( 3 \leq X \leq 6 ) \text { and } P ( X \geq 4 )$ 
c. Using just the pmf, compute P(X>6).

An Insurance Company Offers Its Policyholders a Number of Different