Question

If µ = 100 and δ = 2.5, calculate the following:

a. P(100 < X < 102.1)

b. P(98 < X < 100)

c. P(100 < X)

d. P(102.1 < X)

e. P(98 < X < 102.1)

f. P(X < 102.1)

Answer #1

Please like ?

1. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What is the value of α, i.e.,
maximum probability of Type I error?
A. 0.90 B. 0.10 C. 0.05 D. 0.01
2. For testing H0 : µ = 0 vs. Ha : µ > 0, H0 is rejected if X
>¯ 1.645, given n = 36 and σ = 6. What...

Assume a Poisson distribution. A) If ? = 2.5 , find P(X =2 ). B)
If ? = 0.5find P(X =1) C) If ? = 8.0find P(X=3) D) If ? = 3.7find
P(X =10)

Given the following cumulative probability
function:
0 x < -5
.10 -5 <= x < 0
.40 0 <= x < 5
F(x)= .50 5 <= x < 10
.75 10 <= x < 15
1.0 X >= 15
a. P( 0 <x<10)
b. P( 5<x<10)
c. P(x< 10)
d. P(x>5)
e. P(x=7)
f. Calculate f (x) and draw F (x) and F (x)
g. Calculate E (x)
h. Calculate the variance of X
i. Calculate the expected g (x)...

given P(x)= 2(x-1)(x+1)^2(x+2) answer the following a) what is
the leading term of P(x) b) what is the degree of p(x) c) as x
approaches infinity, the function P(x) _____ d) as x approaches
negative infinity, the function P(x)______ e) how many turning
points does it have? f) what are the coordinates of the x
intercepts? g) find the coordinates of the P intercepts

For a symmetric distribution with mean µ, the mean absolute
deviation is the expected value MAD(X) = E(|X − µ|), of the
absolute difference |X − µ|, which is strictly positive. The mean
absolute deviation for the standard normal distribution is an
integral 1 √ 2π Z ∞ −∞ |x| e −x 2/2 dx = p 2/π = 0.7979....
Part a: Find the MAD of the Bernoulli-1/2 distribution.
Part b: Find the MAD of the binomial distribution Bin(2,
1/2).
Part...

Differentiate the following functions with respect to x
using any applicable rules of differentiation.
(a) P(x) = 300x − 50000
(b) Γ(x) = ryz ∗ tey
_______
logva
(c) h(x) = 5x2 + x½
___________
x
(d) y = Cekt
(e) j(x) = xex
(f) p(x) = (2x2 + x) 3

If X∼Binom(n,p), E[X] = np. Calculate V[X] = np(1−p) by:
a) First show E[X(X−1)] + E[X] − (E[X])^2 = V[X] (Hint: Use
propertie of E[·] and V[·]).
b) Show E[X(X−1)] = n(n−1)p^2
c) Use E[X] = np, a) and b) to discuss, V[X] = np(1−p).

Use ε − δ definition to prove that the function f (x) =
2x/3x^2 - 2 is continuous at the
point p = 1.

Let 'x' be a random variable that represents the length of time
it takes a student to write a term paper for Tonys class. After
interviewing students, it was found that 'x' has an approximately
normal distribution with a mean of µ = 7.3 hours and standard
deviation of ơ = 0.8 hours.
For parts a, b, c, Convert each of the following x
intervals to standardized z intervals.
a.) x < 7.5
z <
b.) x > 9.3
z...

Given the following probability function:
.10 x = 5
f(x) = . 20 x = -2, 8, 10
.30 x = 6
A. Calculate f(x) and make an appropriate drawing of f(x) and
F(x) (15 pts)
B. P (6 < X < 8) (5 pts)
C. P (x > 7) (5 pts)
D. P (x < 8) (5 pts)
E. The average of X (5 pts)
F. The fashion of X (5 pts)
G. The variance of X (10 pts)

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