Question

Assume that X has an exponential distribution with parameter θ = 3.

**A) Find** P(X ≤ 1). Give your answer to 4 decimal
places

**B) Find** P(2 ≤ X ≤ 10). Give your answer to 4
decimal places.

Answer #1

(A)

Probability Density Function of X is given by:

,

for x 0

= 0, for x <0

between limits 0 to 1.

Applying limits, we get:

So,

Answer is:

**0.9502**

(B)

between limits 2 to 10.

Applying limits, we get:

So,

Answer is:

**0.0025**

. X has exponential distribution with parameter 4. Therefore
E[X] = 1/4 .
Find P(X > 6) and P(X > 6|X > 1).
Find E[X|X > 1].
Would someone help me with the correct detail solutions to the
problems

Let we have a sample of 100 numbers from exponential
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f(x, θ) = θ e- θx , 0
< x.
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=
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? = 41; ? = 15
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