STAT 3502 Solution-Sample Midterm Solution: 1. a) 0.27, b) 0.143, c) mean=2, standard deviation=1.41, d) 0.135, e) 0.00148 (use binomial (5,0.865) 2. q 3 p when p=P(win) 3. 0.536, 15/8 4. a) cfw_A, B, AB, No-defect, b) 7/100, c) 5/100, d) 3/100, e) 15/100

STAT 3502 Assignment # 2
Due: 21 June, 2010 prior to the start of class 1. Two fair six-sided dice are tossed independently. Let M = maximum of the two tosses. a. [2] What is the pmf of M? b. [2] Determine the cdf of M and graph it. a. the pmf of M is: b.

CHAPTER 3
Random Variable A rule that associate a number to each outcome of an experiment (or each outcome in S ) is random variable. Bernoulli random variable: Any random variable whose only possible values are 0 and 1 Example: Give three examples of Ber

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4
Continuous Random Variables and Probability Distributions
INTRODUCTION
Chapter 3 concentrated on the development of probability distributions for discrete random variables. In this chapter, we study the s

STAT 3502 Solution for Assignment # 4 Due: 19 July, 2010 prior to the start of class
Total mark=25
1. Suppose that a random sample of size n is drawn from the Bernoulli distribution f ( x; p ) = px (1 p)1x 0 x = 0, 1 otherwise.
Find a maximum likelihood e

STAT 3502 Solution for assignment # 1
Total mark=25
1. For hard drives to operate properly, the distance between the read/write head and the disk must remain between tight limits. From each hours production, 40 drivers are selected and the distance is mea

STAT 3502 Solution for assignment # 2
Total mark=25
1. Two fair six-sided dice are tossed independently. Let M = maximum of the two tosses. a. [2] What is the pmf of M ? b. [2] Determine the cdf of M and graph it. Sol:
2. [2] Let x = the outcome when a fa

Solutions Test 1 PHYS 1004 Summer 2010 1. The Coulombs force between two protons is F = 3 108 N when the distance between them is ( in m) Fc = k (e)2 /r 2 so r = k e2 /F = 8.76 1011 . 2. A metallic sphere of radius 20 cm is charged to surface charge densi

1/ (a)
& & = & k t i - b - k = J J
& Vin = iR + eb = iR + k t
i =
& Vin - k t R
& V - k t & k t in - b - k R & & = J
2 & + k t / R + b + k = k t V & in J J RJ (b) H ( s) = kt / RJ (k / R) + b s2 + t s+k/J J
2
(
)
(c) i) When the derivates are set to zero

STAT 3502 Assignment # 3 Total mark=25 Due: 19 July, 2010 prior to the start of class
1. If two random variables have the joint density f (x, y ) =
6 (x 5
+ y2)
0
0 < x < 1, 0 < y < 1 otherwise.
a. [1] Find the probability that 0.2 < X < 0.5 and 0.4 < Y <

STAT3502
Solution for assignment # 3
1. a. E (X ) = xi P (xi ) = 0.2 + 0.2 + 0.15 = 0.55 V (X ) = x2 p(xi ) 2 = 0.2 + 0.4 + 0.45 (0.55)2 = 0.7475 i x = 0.7475 = 0.865 b. c. Skewed to the right. Based on the CLT Shape of distribution of X is normal (bell s

Solution for assignment # 2 1. a) = 2, P (X 2) = 1 P (X 1) = 0.594
b) = 4, P (X = 0) = e4 = 0.018 c) P (X = 0|10 calls before) = P (X = 0) = 0.018, because the # of events in any interval are independent from that of any other mutually exclusive interval

STAT 3502 Assignment # 2 Total mark=25 Due: 21 June, 2010 prior to the start of class
1. Two fair six-sided dice are tossed independently. Let M = maximum of the two tosses. a. [2] What is the pmf of M ? b. [2] Determine the cdf of M and graph it. 2. [2]

STAT 3502 Assignment # 4 Total mark=25 Due: 9 August, 2010 prior to the start of class
1. Suppose that a random sample of size n is drawn from the Bernoulli distribution f ( x; p ) = px (1 p)1x 0 x = 0, 1 otherwise.
Find a maximum likelihood estimator of

Note: all denitions are from your textbook
CHAPTER 1
What is Statistics? The discipline of statistics teaches us how to make intelligent judgments and informed decision in the presence of uncertainty and variation. Branches of Statistics
Descriptive Stat

CHAPTER 2
PROBABILITY Probability is used in inference statistics as a tool to make statement for population from sample information. Experiment is a process for generating observations Sample space is all possible outcomes of an experiment. Event is a co

CHAPTER 4 Continuous Random Variables and Probability Distributions
Basic denitions and properties of continuous random variables Continuous random variable: A random variable is continuous if its set of possible values is an entire interval of numbers. P

PHYS 1004 Summer 2010 MIDTERM Solutions
Wed. July 28th
7:00 -8:30 PM
Multiple choice questions, 3 points each, answer 10 : ( circle the answer closest to the correct result) 1. Chose the dipole with highest potential energy with respect to constant extern

STAT 3502 Sample Midterm 1. A certain type of circuit board contains 200 diodes that function independently of each other. Each diode has probability 0.01 of failing. a. What is the approximate probability that exactly two diodes will fail? b. What is the

Solution for assignment # 1 1. a) X = b) = 185.377 P.O.M = 0.5(31 + 1) = 16 X = 150.58 Since there is no outlier in this set of data, so mean is more appropriate than
X2
( Xi ) 2
Xi n
=
5746.7 31
median. (Upper fence is 491.56).
i n c) S 2 = = 30 n1 2= S=

STAT 3502 Assignment # 4 Total mark=25
Fengbo Cui 100719108 Aug 9, 2010
2. In a survey of 4720 American, 708 of them were overweight. calculate and interpret a 99% confidence interval for the proportion of all American who are overweight.[3] n= 4720 X=708