Question

Based on the number of voids, a ferrite slab is classied as either high, medium, or low. Historically, 5% of the slabs are classied as high, 90% as medium, and 5% as low. A sample of 20 slabs is selected for testing. Let X; Y; and Z denote the number of slabs that are independently classied as high, medium, and low, respectively

a. What is the joint probability distribution of X; Y; and Z and what are it's parameteres (n,p1...)?

b. What is the range of the joint probability distribution of X; Y , and Z?

c. What are the name and the values of the parameters of the marginal probability distribution of X?

d. Calculate E(X) and V (X).

Determine the following:

e. P(X = 1; Y = 17;Z = 3)

f. P(X<=1; Y = 17;Z = 3)

g. P(X<= 1)

h. E(Y )

i. P(X = 2;Z = 3 I Y = 17)

j. P(X = 2 I Y = 17)

k. E(X I Y = 17)

Answer #1

Based on the number of voids, a ferrite slab is classified as
either high medium or low. Historically, 5% of the slabs are
classified as high, 83% as medium and 12% as low. A sample of 20
slabs is selected for testing. Let X, Y, and
Z denote the number of slabs that are independently
classified as high, medium, and low, respectively. Determine the
following. Round your answers to four decimal places (e.g.
98.7654).
(a) P(X = 1, Y =...

Based on the number of voids, a ferrite slab is classified as
either high medium or low. Historically, 5% of the slabs are
classified as high, 80% as a medium, and 15% as low. A sample of 20
slabs is selected for testing. Let X, Y, and
Z denote the number of slabs that are independently
classified as high, medium, and low, respectively. Determine the
following. Round your answers to four decimal places (e.g.
98.7654).
(a) P(X = 1, Y...

The backoff torque required to remove bolts in a steel plate is
rated as high, moderate, or low. Historically, the probability of a
high, moderate, or low rating is 0.61, 0.25, or 0.14, respectively.
A sample of 15 bolts are selected for testing. Let X,
Y, and Z denote the number of bolts that are
independently rated as high, moderate, and low, respectively.
Determine the following probabilities.
(a)
P(X = 11, Y = 2, Z =
2)
(b)
P(X =...

Motivation Level
Talent
High
Medium
Low
Total
High
6
18
6
Medium
21
35
6
Low
12
6
2
Total
Q1. Are high motivation and high talent independent? Justify
your answer.
Adrian sells cars for Honest Joe’s car dealership. Adrian has
never sold more than three cars in a given week. Given X is the
number of cars sold by Adrian in a week, the probability
distribution of X is summarized in the following table:
X
0
1
2
3...

Suppose that the number of eggs that a hen lays follows the
Poisson distribution with parameter λ = 2. Assume further that each
of the eggs hatches with probability p = 0.8, and different eggs
hatch independently. Let X denote the total number of survivors.
(i) What is the distribution of X? (ii) What is the probability
that there is an even number of survivors? 1 (iii) Compute the
probability mass function of the random variable sin(πX/2) and its
expectation.

Suppose that a person plays a game in which he draws a ball from
a box of 10 balls numbered 0 through 9. He then puts the ball back
and continue to draw a ball (with replacement) until he draws
another number which is equal or higher than the first draw. Let X
denote the number drawn in the first draw and Y denote the number
of subsequent draws needed.
(a) Find the conditional probability distribution of Y given X...

A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly
(the tosses are independent). Deﬁne (X = number of the toss on
which the ﬁrst H appears, Y = number of the toss on which the
second H appears. Clearly 1X<Y. (i) Are X and Y independent?
Why or why not? (ii) What is the probability distribution of X?
(iii) Find the probability distribution of Y . (iv) Let Z = Y X.
Find the joint probability mass function

A coin with P[Heads]= p and P[Tails]= 1p is tossed repeatedly
(the tosses are independent). Deﬁne (X = number of the toss on
which the ﬁrst H appears, Y = number of the toss on which the
second H appears. Clearly 1X<Y. (i) Are X and Y independent?
Why or why not? (ii) What is the probability distribution of X?
(iii) Find the probability distribution of Y . (iv) Let Z = Y X.
Find the joint probability mass function

Suppose that the number of eggs that a hen lays follows the
Poisson distribution with parameter λ = 2. Assume further that each
of the eggs hatches with probability p = 0.8, and different eggs
hatch independently. Let X denote the total number of
survivors.
(i) What is the distribution of X?
(ii) What is the probability that there is an even number of
survivors?
(iii) Compute the probability mass function of the random
variable sin(πX/2) and its expectation.

The joint probability distribution of the number X of
cars and the number Y of buses per signal cycle at a
proposed left-turn lane is displayed in the accompanying joint
probability table.
y
p(x,
y)
0
1
2
x
0
0.010
0.015
0.025
1
0.020
0.030
0.050
2
0.050
0.075
0.125
3
0.060
0.090
0.150
4
0.040
0.060
0.100
5
0.020
0.030
0.050
(a) What is the probability that there is exactly one car and
exactly one bus during...

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