Question
In: Statistics and Probability
Suppose that X is a Poisson random variable with λ=39. Round your answers to 3 decimal...
Suppose that X is a Poisson random variable with λ=39.
Round your answers to 3 decimal places (e.g. 98.765).
(a) Compute the exact probability that X is less than 26.
(b) Use normal approximation to approximate the probability that X is less than 26.
Without continuity correction:
With continuity correction:
(c) Use normal approximation to approximate the probability that 52<X<78.
Without continuity correction:
With continuity correction:
Solutions
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orchestra answered 1 year agoRelated Solutions
1 x is a binomial random variable. (Give your answers correct to three decimal places.) (a)...
1
x is a binomial random variable. (Give your answers
correct to three decimal places.)
(a) Calculate the probability of x for:
n = 7,
x = 3, p =
0.9
P(x) =
(b) Calculate the probability of x for:
n = 5,
x = 4, p =
0.25
P(x) =
(c) Calculate the probability of x for:
n = 8,
x = 2, p =
0.6
P(x) =
(d) Calculate the probability of x for:
n = 6,
x...
1. x is a binomial random variable. (Give your answers correct to three decimal places.) (a)...
1. x is a binomial random variable. (Give your answers correct
to three decimal places.)
(a) Calculate the probability of x for: n = 1, x = 0, p = 0.35
(b) Calculate the probability of x for: n = 7, x = 6, p = 0.7
(c) Calculate the probability of x for: n = 4, x = 1, p =
0.35
(d) Calculate the probability of x for: n = 3, x = 3, p =
0.7
(e)...
Question: (Bayesian) Suppose that X is Poisson(λ + 1), and the prior distribution of λ is...
Question:
(Bayesian) Suppose that X is Poisson(λ + 1), and the prior
distribution of λ is binomial(2,1/3).
(a) Find the Bayesian estimate of λ for mean square loss based
on the single observation X, if X = 1.
(b) Find the Bayesian estimate of λ for mean square loss based
on the single observation X, if X = 2
Hints:
Because of its prior distribution, λ can take only three values,
0,1,2.
Don’t expect its posterior distribution to be any...
Find the value x for which: (Round your answers to 3 decimal places. You may find...
Find the value x for which: (Round your answers
to 3 decimal places. You may find it useful to reference the
appropriate table: chi-square table or F table)
x
a.
P( χ^2 25 ≥ x) = 0.005
b.
P( χ^2 25 ≥ x) = 0.010
c.
P( χ^2 25 < x) = 0.005
d.
P( χ^2 25 < x) = 0.010
Find the value x for which: (Round your answers to 3 decimal places. You may find...
Find the value x for which: (Round your answers to 3 decimal
places. You may find it useful to reference the appropriate table:
chi-square table or F table) x a
. P( χ217 ≥ x) = 0.900 b. P( χ217 ≥ x) = 0.950 c. P(
χ217 < x) = 0.900 d. P( χ217 < x) = 0.950
Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.)
Given that z is a standard normal random variable, find z for each situation. (Round your answers to two decimal places.)
(a)
The area to the left of z is 0.1841.
(b)
The area between −z and z is 0.9398.
(c)
The area between −z and z is 0.2052.
(d)
The area to the left of z is 0.9948.
(e)
The area to the right of z is 0.6915.
Let Y denote a random variable that has a Poisson distribution with mean λ = 6....
Let Y denote a random variable that has a Poisson
distribution with mean λ = 6. (Round your answers to three
decimal places.)
(a) Find P(Y = 9).
(b) Find P(Y ≥ 9).
(c) Find P(Y < 9).
(d) Find P(Y ≥
9|Y ≥ 6).
Show that the skewness of X~Poisson(λ) is λ^-(1/2)
Show that the skewness of X~Poisson(λ) is λ^-(1/2)
Suppose X1, X2, . . ., Xn are iid Poisson random variables with parameter λ. (a)...
Suppose X1, X2, . . ., Xn are iid Poisson random variables with
parameter λ.
(a) Find the MVUE for λ.
(b) Find the MVUE for λ 2
Given are five observations for two variables, x and y. (Round your answers to two decimal...
Given are five observations for two variables, x and y. (Round
your answers to two decimal places.) xi 1 2 3 4 5 yi 3 8 6 11 14
(a) Use sŷ* = s 1 n + (x* − x)2 Σ(xi − x)2 to estimate the standard
deviation of ŷ* when x = 3. Incorrect: Your answer is incorrect.
(b) Use ŷ* ± tα/2sŷ* to develop a 95% confidence interval for the
expected value of y when x = 3....
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