Question

2. Let X be a Normal random variable with µ = 11 and σ 2 = 49. You may refer to the tables at the end of our textbook.

(a) Calculate P(X2 > 100).

(b) Calculate the hazard rate function at 18, λ(18) and at 25, λ(25).

Answer #1

Let X be a Normal random variable with µ = 11 and
variance = 49.
a) Calculate P(X^2>100)
b)Calculate the hazard rate function at 20, λ(20) and
at 35, λ(35)

Let the random variable X follow a normal distribution with µ =
18 and σ = 4. The probability is 0.99 that X is in the symmetric
interval about the mean between two numbers, L and U (L is the
smaller of the two numbers and U is the larger of the two numbers).
Calculate L.

Let the random variable X follow a normal distribution
with µ = 22 and σ = 4. The probability is 0.90
that Xis in the symmetric interval about the mean between
two numbers, L and U (L is the smaller of the two numbers and U is
the larger of the two numbers). Calculate U.

Let the random variable X follow a normal distribution with µ =
18 and σ2 = 11. Find the probability that X is greater than 10 and
less than 17.

Let X1, X2 be two normal random variables each with population
mean µ and population variance σ2. Let σ12 denote the covariance
between X1 and X2 and let ¯ X denote the sample mean of X1 and X2.
(a) List the condition that needs to be satisﬁed in order for ¯ X
to be an unbiased estimate of µ. (b) [3] As carefully as you can,
without skipping steps, show that both X1 and ¯ X are unbiased
estimators of...

Let the random variable X follow a normal distribution with µ =
19 and σ2 = 8. Find the probability that X is greater than 11 and
less than 15.

Let X ∼ N (µ, σ^2). Prove that P (|X − µ| > kσ) does not
depend on µ or σ.
Please write your answer as clearly as you can, appreciate
it!

Let X be a normal random variable with
μ=15 and σ=2.3
Find: P(X less than or equal to 16)
Answer choices
a. .023
b. .357
c. .332
d. .455
e. .668
P(X≤16).P(X≤16).
Drawing a picture may be helpful.

Suppose X is a normal random variable with μ =
60 and σ = 5. Find the values of the following
probabilities. (Round your answers to four decimal places.)
(a) P(X < 65)
(b) P(X > 46)
(c) P(58 < X <
67)
You may need to use the appropriate table in the Appendix of Tables
to answer this question.

Suppose X is a normal random variable with μ =
300 and σ = 40. Find the values of the following
probabilities. (Round your answers to four decimal places.)
(a) P(X < 414)
(b) P(340 < X <
408)
(c) P(X > 340)
You may need to use the appropriate table in the Appendix of Tables
to answer this question.

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