Suppose X has an exponential distribution with mean equal to 11. Determine the following: (a) (Round your answer to 3 decimal places.) (b) (Round your answer to 3 decimal places.) (c) (Round your answer to 3 decimal places.) (d) Find the value of x such that . (Round your answer to 2 decimal places.)

Step-by-step explanation:

Given

--- Mean

Required (Missing from  the question)

(d) x such that

In an exponential distribution:

--- the pdf

--- the cdf

In the above equations:

Substitute 11 for E(x)

Now, we solve (a) to (d) as follows:

Solving (a): P(X>11)

Substitute 11 for x in

Remove bracket

Solving (b): P(X>22)

Substitute 22 for x in

Remove bracket

Solving (c): P(X>33)

Substitute 33 for x in

Remove bracket

Solving (d): x when

Here, we make use of:

Substitute

So, we have:

Subtract 1 from both sides

Reorder the equation

Substitute 1/11 for

Solve for x:

--- approximated

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

good luck on your studies! : )

david edward.