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A Discussion On E(X) and Var(X) of X

Let x be a random variable with the following probability distribution: Value x of X......P(X = x) ........-1...............0.05 .........0...............0.05 .........1...............0.60 .........2...............0.05 .........3...............0.15 .........4...............0.10 Find the expectation E(X) an

Probabilities: Senior or Business Major

Suppose that a certain college class contains 59 students. Of these, 35 are seniors, 30 are business majors, and 12 are neither. A student is selected at random from the class. a. What is the probability that the student is both a senior and a business major? b. Suppose that we are given the additional information that the s

Probabilities: Random Selection Problems

Please help with the following problems. Provide step by step calculations. At a certain college, 51% of the students are female and 17% of the students major in civil engineering. Furthermore, 10% of the students both are female and major in civil engineering. a. What is the probability that a randomly selected female stu

Statistics Control charts, probabilities

This is for Quality Control Consider the xbar chart for the piston-ring example as follows, let ring diameter be normally distributed, and the sample size is n = 5. a) Find the two-sigma control limits for this chart. b) Suppose it was suggested that the two-sigma limits be used instead of the typical three-sigma limits.


Please see the attached file for full problem description.

Mutually exclusive and independant events

Please see the attachment for the question. Let B and C be two events such that P(B) = 0.50 and P(C) = 0.05. a. Determine P(B U C), given that B and C are mutually exclusive. b. Determine P(B U C), given that B and C are independent.


Suppose that A and B are independent events such that P(A)=0.30 and P(B)=0.40. Find the following probabilities... (see attachment for full question)

Probability distribution function

Please see the attached file for full problem description with all proper "X" symbols. --- Can you show me how to complete this kind of problem? Suppose that the genders of the three children of a certain family are soon to be revealed. Outcomes are thus triples of "girls" ( ) and "boys" ( ), which we write , , etc. For ea

Normal distribution, probabilities (3 problems)

Problem 1 We know the IQ of people is normally distributed with mean 120 and standard deviation (SD) of 25. Calculate the probability that an adult will have a ) IQ less than 100 b) IQ greater than 150 c) IQ between 100 and 150 d) Any person with a score over 200 is considered a genius. In a population of 10000

Odds Ratio. A verbal interpretation of the results of a study on smoking.

Those who have quit smoking often return to the habit. The authors of a paper concluded that forbidding smoking in the smoker's residence was a significant predictor of the ability to abstain from smoking. They collected data, calculated statistics, and presented the following as support for their conclusion: OR=1.95 C.I.


PROBLEM 4 Out of 11 people applying for an assembly job, 3 cannot do the work. Suppose two persons will be hired. (a) How many distinct pairs are possible? (b) In how many of the pairs will 0 or 1 people not be able to do the work? (c) If two persons are chosen in a random manner, what is the probability that neither will b


PROBLEM 3 Items coming off a production line are categorized as good (G), slightly blemished (B), and defective (D), and the percentages are 80%, 15% and 5%, respectively. Suppose that two items will be randomly selected for inspection and the selections are independent. (a) List all outcomes and assign probabilities. (b) Fin


PROBLEM 1 PART ONE In a shipment of 15 room air conditioners, there are 3 with defective thermostats. Two air conditioners will be selected at random and inspected one after another. Find the probability that (a) The first is defective. (b) The first is defective and the second is good. (c) Both are defective. (d) The sec


Records of student patients at a dentist's office concerning fear of visiting the dentist suggest the following proportions: (see attachment for full question).


Suppose P(A)= 0.55, P (B)= 0.32 and P( ) = 0.20 (see attachment for full question)

What is the probability that an assembly will have exactly one defect? What is the probability that it contains one or more nonconformances? How many would have a tensile strength in excess of 48 lb? What fraction of these batteries would be expected to survive beyond 1000 days?

2-17 A mechatornic assembly is subjected to a final functional test. Suppose that defects occur at random in these assemblies, and that defects occur according to a Poisson distribution with parameter = 0.02 a) What is the probability that an assembly will have exactly one defect? b) What is the probability that an assemb




For two events A and B, the following probabilities are specified. P (A) = 0.52 P (B) = 0.36 P (AB) =0.20 (a) Enter these probabilities in the following table, See attached file for full problem description.


A sample space consists of 8 outcomes with the following probabilities. See attached file for full problem description.


Suppose you are eating at a pizza parlor with two friends. You have agreed to the following rule about who will pay the bill: Each person will toss a coin. The person who gets a result that is different from the other two will pay the bill. If all three tosses yield the same result, the bill will be shared by all. Find the proba


Let X1 and X2 be two independent standard normal random variables. Let Y1 = X1+X2 and Y2=X1/X2. a) Find the joint density of Y1 and Y2 b) Find the marginal density of Y1 and Y2 (The distribution of Y2 is known as the Cauchy distribution).


Suppose X1 and X2 are independent exponential (λ) random variables. Let Y1=X1-X2 and Y2=X2. a) Find the joint density of Y1 and Y2. b) Find the marginal density of Y1.


Suppose X and Y are independent chi-square random variables with m and n degrees of freedom respectively. Let U = (X/m) / (Y/n) a) Find the density of U (The distribution of U is called the F-Distribution with m and n degrees of freedom). b) Find the density of V = U / (1+U)

Joint Probabilities

Let Z be a standard normal random variable and let V have a chi-square distribution with n-degrees of freedom. Assume that Z and V are independent and let T = Z / √ (V/n) Find the density of T (The distribution of T is known as the t-distribution with n degrees of freedom.)


Find the probability for the various situations

New Source, Inc. - Probability

NewSource Inc. uses natural gas in its production-processing operations. Neighboring companies in its upstate Ohio area have successfully drilled for gas on their premises, and NewSource is considering following suit. Their initial expenditure would be drilling, which would cost $80,000. If they strike gas, they would have to

Probability of Events: Sum Rule

Our psychology department received a new statistics text for review. Prof. Smart in his review provided an interesting table of corrections. Type: Alterations: 20%, Spelling 50%, Spelling and alterations: 10%. Assuming that spelling and alterations are the only possible types of corrections, calculate the probability of spot