a$)$ Calculate the probability that a person has been unemployed for two months or less $($i$.$e$.,$ P$($ X

Submit your answer by choosing one of the following options from the drop$-$down menus given below.

Option $1$: $0\mathrm{.}120$

Option $2$: $0\mathrm{.}164$

Option $3$: $0\mathrm{.}142$

Option $4$: $0\mathrm{.}087$

Option $5$: $0\mathrm{.}197$

b$)$ Calculate the probability that a person has been unemployed for more than $2$ months $($i$.$e$.,$ P$($ X $>2)).$

Submit your answer by choosing one of the following options from the drop$-$down menus given below.

Option $1$: $0\mathrm{.}858$

Option $2$: $0\mathrm{.}869$

Option $3$: $0\mathrm{.}891$

Option $4$: $0\mathrm{.}814$

Option $5$: $0\mathrm{.}902$

c$)$ Calculate the probability that a person has been unemployed for more than $5$ months $($i$.$e$.,$ P$($ X $>5)).$

Submit your answer by choosing one of the following options from the drop$-$down menus given below.

Option $1$: $0\mathrm{.}427$

Option $2$: $0\mathrm{.}394$

Option $3$: $0\mathrm{.}383$

Option $4$: $0\mathrm{.}361$

Option $5$: $0\mathrm{.}339$

d$)$ Calculate the expected value for the length of unemployment $($i$.$e$.,$ E$[$X$]).$

Submit your answer by choosing one of the following options from the drop$-$down menus given below.

Option $1$: $4\mathrm{.}934$

Option $2$: $4\mathrm{.}967$

Option $3$: $4\mathrm{.}989$

Option $4$: $4\mathrm{.}978$

Option $5$: $4\mathrm{.}956$

e$)$ Calculate the variance for the length of unemployment $($i$.$e$.,$ Var$[$X$]).$

Submit your answer by choosing one of the following options from the drop$-$down menus given below.

Option $1$: $5\mathrm{.}097$

Option $2$: $5\mathrm{.}053$

Option $3$: $5\mathrm{.}042$

Option $4$: $4\mathrm{.}987$

Option $5$: $4\mathrm{.}998$