Answer:
Step-by-step explanation:
From the missing information;
Lets assume that;
[tex]\text{the exponential distribution mean = 500 thousand naira}[/tex]
[tex]\text{Range 100 thousand}[/tex] → [tex]\text{1 million naira}[/tex]
∴
a)
[tex]X \sim exp (\dfrac{1}{500}) \\ \\ P( X \le x) = 1 - e^{\dfrac{-x}{500}} \\ \\ P(X < 700) = 1 - e^{\frac{-7}{5}} \\ \\ \mathbf{P(X< 700) = 0.75340}[/tex]
b)
[tex]Y \sim \cup (100,1000) \implies P(Y \le y ) = \dfrac{y - 100}{1000-100} \\ \\ P(Y < 700) = \dfrac{600}{900} = 0.67[/tex]
c)
[tex]P(X < 830)= 1 - e^{\frac{-830}{500}} \\ \\ P(X < 830)= 1 - 0.1901 \\ \\ P(X < 830)=0.8099 \\ \\ P(Y < 830) = \dfrac{730}{900} = 0.8111 \\ \\ Thus;\mathbf{ P(X < 0.8099) = P(Y< 0.8111)}[/tex]
