Deadline:
For DL Students: 15th march
For Regular Students: 10th march

Source: Textbook
Q 4-5,
Find xu for u= 0.1, 0.2 … 0.9
a) if x is uniform in the interval (0,1);
b) if f(x)= 2e-2x U(x)

Q 4-7,
Show that if the uniform variable x has an Erlang density with n=2, then Fx(x) = (1-e-cx-cxe-cx) U(x)

Q 4-8,
The random variable x is N (10; 1), Find f (x | (x-10)2 <4)

Q 4-9,
Find f(x) if F(x) = (1-e-ax) U(x-c).

Q 4-10,
If x is N (0, 2) find
a) P{1≤ x ≤ 2}
b) P{1≤ x ≤2 | x ≥ 1}

Q4-14,
A fair coin is tossed 900 times and the random variable x equals the total number of heads. a) Find fx(x), 1: exactly, 2: approximately Gamma Distribution eq. b) Find P {435 ≤ x ≤ 460}.

Q4-25,
If P (A) = 0.6 and k is the number of successes of A in n trials, a) Show that P {550 ≤ k ≤ 650} = 0.999, for n=1000.
b) Find n such that P {0.59n ≤ k ≤ 0.61n} = 0.95

Q 4-26,
A system has 100 components. The probability that a specific component will fail in the interval (a, b) equals e-a/T – e-b/T. Find the probability that in the interval (0, T/4), no more than 100 components will fail.

...Exercise
Chapter 3 Probability Distributions
1. Based on recent records, the manager of a car painting center has determined the following probability distribution for the number of customers per day. Suppose the center has the capacity to serve two customers per day.
|x |P(X = x) |
|0 |0.05 |
|1 |0.20 |
|2 |0.30 |
|3 |0.25 |
|4 |0.15 |
|5 |0.05 |...

...Math 107 002
Homework 5 (due 13 Oct 2011)
Fall 2011
Please use your calculators and give your ﬁnal answers to 3 signiﬁcant ﬁgures. Show your work for full credit. Please state clearly all assumptions made.
1. Classify each randomvariable as discrete or continuous. (a) The number of visitors to the Museum of Science in Boston on a randomly selected day. (b) The camber-angle adjustment necessary for a front-end alignment. (c) The total number of pixels in a...

...SIDS31081 - Statistics Refresher
2006 – 2007
Exercises
(Probability and RandomVariables)
Exercise 1
Suppose that we have a sample space with five equally likely experimental outcomes :
E1,E2,E3,E4,E5.
Let
A = {E1,E2}
B = {E3,E4}
C = {E2,E3,E5}
a. Find P(A), P(B), P(C).
b. Find P(A U B) . Are A and B mutually exclusive?
c. Find Ac, Bc, P(Ac), P(Bc).
d. Find A U Bc and P(A U Bc)
e. Find P(B U C)
Exercise 2
A committee with two members is to be...

...selected at random from the sample.
a) What is the probability the person is female or occasionally involved in charity work?
b) Are the events “being female and occasionally involved in charity work” and “being frequently involved in charity work” mutually exclusive?
yes
6. A company gave psychological tests to perspective employees. The randomvariable x represents the possible test scores.
a) Use the histogram to find...

...of 4 messages sent by Alice to Bob at least one is not forged?
Event A is selecting a “red” card from a standard deck at random. Suggest another event (Event B) that is compatible with Event A.
What is the probability of getting 6 tails in 10 trials of tossing a coin? Solve this problem by using :The approximation mentioned in Theorem 6
The Binomial Distribution
Then compare answers for a) and b) after you have solved the problem.
When transmitting...

...of tires and assign a quality rating to each tire on a 3-point
scale. Let X denote the rating given by expert A and Y denote the rating given by B. The following table
gives the joint distribution for X and Y .
4.12 If a dealer’s proﬁt, in units of $5000, on a new automobile can be looked upon as a randomvariable
X having the density function
fx= 21-x,0<x<10,elsewhere
ﬁnd the average proﬁt per automobile.
4.14 Find the proportion X of...

...THE MOMENTS OF A RANDOMVARIABLE
Definition: Let X be a rv with the range space Rx and let c be any known constant. Then the kth moment of X about the constant c is defined as
Mk (X) = E[ (X c)k ]. (12)
In the field of statistics only 2 values of c are of interest: c = 0 and c = . Moments about c = 0 are called origin moments and are denoted by k, i.e., k = E(Xk ), where c = 0 has been inserted...

...continuous randomvariable because the time is being measured. All possible results for the variable time (t) would be greater than > 0.
b) The weight of a T-bone steak is a continuous randomvariable because the weight of the steak is measured. All the possible results for the weight of the T-bone steak would be positive numbers making the variable weight (w) > greater than 0....

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