If X is a normal random variable with parameters σ2 = 36 and μ =
10,...
If X is a normal random variable with parameters σ2 = 36 and μ =
10, compute (a) P{X ≥ 5} .
(b) P{X = 5}.
(c) P{10>X≥5}.
(d) P{X < 5}.
(e) Find the y such that P{X > y} = 0.1.
let the random variable x follow a normal distribution with μ =
50 and σ2 = 64.
a. find the probability that x is greater than 60.
b. find the probability that x is greater than 35 and less than
62
. c. find the probability that x is less than 55.
d. the probability is 0.2 that x is greater than what
number?
e. the probability is 0.05 that x is in the symmetric interval
about the mean between...
et the random variable x follow a normal distribution with μ =
50 and σ2 = 64.
a. find the probability that x is greater than 60.
b. find the probability that x is greater than 35 and less than
62 .
c. find the probability that x is less than 55.
d. the probability is 0.2 that x is greater than what
number?
e. the probability is 0.05 that x is in the symmetric interval
about the mean between...
1. Let X have a normal distribution with parameters μ = 50 and
σ2 =
144. Find the probability that X produces a value between 44 and
62. Use the
normal table A7 (be sure to show your work).
2. Let X ~ Exponential( λ ), for some fixed constant λ > 0.
That is,
fX(x) = λ e-λx = λ exp( -λx ), x > 0, ( fX(x) = 0
otherwise)
(a) Create a transformed random variable Y =...
Let X be a random variable with mean μ and variance σ2.
Given two independent random samples of sizes n1
= 9 and n2
= 7, with sample means X1-bar
and X2-bar,
if
X-bar = k X1-bar
+ (1 – k) X2-bar,
0 < k < 1, is an unbiased estimator for μ. If X1-bar
and X2-bar
are independent, find the value of k that minimizes the standard
error of X-bar.
If X is a normal random variable with mean ( μ ) = 50 and
standard deviation ( σ ) = 40, then the probability of X > 80
is: a. 0.0000 b. 0.7734 c. 1.0000 d. 0.2266
Let the random variable X follow a normal distribution with a
mean of μ and a standard deviation of σ. Let 1 be the mean of a
sample of 36 observations randomly chosen from this population, and
2 be the mean of a sample of 25 observations randomly chosen from
the same population.
a) How are 1 and 2 distributed? Write down the form of the density
function and the corresponding parameters.
b) Evaluate the statement:
?(?−0.2?< ?̅1 < ?+0.2?)<?(?−0.2?<...
Suppose X1, . . . , Xn is a random sample from the Normal(μ, σ2)
distribution, where μ is unknown but σ2 is known, and it is of
interest to test H0: μ = μ0 versus H1: μ ̸= μ0 for some value μ0.
The R code below plots the power curve of the test
Reject H0 iff |√n(X ̄n − μ0)/σ| > zα/2
for user-selected values of μ0, n, σ, and α. For a sequence of
values of μ,...
Let X ∼ Normal(μ = 20, σ2 = 4).
(a) Give the mgf MX of X.
(b) Find the 0.10 quantile of X.
(c) Find an interval within which X lies with probability
0.60.
(d) Find the distribution of Y = 3X −10 by finding the mgf MY of
Y
2] Let x be a continuous random variable that has a normal
distribution with μ = 48 and σ = 8 . Assuming n N ≤ 0.05 , find the
probability that the sample mean, x ¯ , for a random sample of 16
taken from this population will be between 49.64 and 52.60 .
Round your answer to four decimal places.