(a) (b) Find E(W). Find Var(W).

Q: a) The probability of a defective piece being produced in a manufacturing process is 0.01. calculate…

A: Probability of defective piece(p)=0.01Probability of non-defective piece(q)=1-p=1-0.01=0.99Note: You…

Q: Prove that if X and Y are non-negative independent random variables, then X^2 ⊥ Y ^2.

A: To prove that if X and Y are non-negative independent random variables, then X^2 and Y^2 are…

Q: 5) The width of bolts of fabric is normally distributed with mean 950 mm and standard deviation 10…

A: Mean() = 950 mmStandard deviation() = 10

Q: wo random variables, x and y, with values 0, 1, or 2, have the joint probability mass fun n in the…

A: We have a joint probability mass function of two random variable X and Y is given as…

Q: A fair coin is tossed 27 times. What is the probability that at most 24 heads occur? A) 0.99999718…

A: From the provided information,

Q: The probability of having 3 boys out of 4 children is to be determined.  A simulation is conducted…

A: The provided information is as follows:The total number of children is .The experimental probability…

Q: Let X be a continuous random variable with cumulative distribution function given by F(x)=-…

A: The CDF of X:-

Q: Use the Standard Normal Table or technology to find the z-score that corresponds to the following…

A: Use the Standard Normal Table or technology to the z-score that corresponds to the following…

Q: Suzan sees a bag of marbles; she grabs a handful at random. She has seen a bag containing 4 red…

A: 4 red marbles, 3 green ones,2 white ones,1 purple one

Q: Let X follow a normal distribution with mean 4.7 and unknown standard deviation. If P(X < 9.6) =…

A: Given that

Q: What is the probability of drawing a spade from a deck of playing cards 6 or fewer times in 12…

A: There are 52 cards in standard deck of cards.4 suits in deck of cards , each suit have 13…

Q: Construct the indicated confidence interval for the population mean u using the t-distribution.…

A: Given,

Q: There are 8 balls of which 2 are white and 6 red. For the first time, 2 balls are taken from the…

A: Total balls = 8 White balls = 2 Red balls = 6 First time : 2 balls are taken from the bag Than 2…

Q: A pair of fair dice are rolled. What is the probability of their sum being at most 5?

A:

Q: Blood type AB is found in only 3% of the population.† If 200 people are chosen at random, find the…

A: We have given thatn = 200p = 3% = 0.03X ~Binomial(n, p) X ~ Binomial (200, 0.03)

Q: Suppose that there are 10 white marbles, 21 black marbles and 15 purple marbles in an urn. One…

A:

Q: The data given to the right includes data from 43 candies, and 5 of them are red. The company that…

A: Sample size n=43Favorable cases x=5Sample proportion p^=x/n=5/43=0.1163

Q: A random variable X has cumulative distribution function

A: A random variable X has cumulative distribution function is,

Q: Two wine tasters rate each wine that they taste on a scale of 1 to 5. From data on their ratings of…

A: The data set of two wine tasters rated each wine that they tasted on a scale of 1 to 5.The…

Q: Once an individual has been infected with a certain disease, let X represent the time (days) that…

A: Let f be a pdf ; x&gt;=0= 0 ; x&lt;0

Q: 3) The grade point averages of a large population of college students is approximately normally…

A: Let X be the grade point average of large population of college students.Given, X is approximately…

Q: Let the probability of success on a Bernoulli trial be 0.30. a. In five Bernoulli trials, what is…

A: The probability of success on a Bernoulli trial is 0.30.

Q: A manufacturer knows that their items have a lengths that are skewed right, with a mean of 15.2…

A: Mean()=15.2Standard deviation()=3.1Sample size(n)=48

Q: The data given to the right includes data from 42 candies, and 10 of them are red. The company that…

A: Sample size n=42Favorable cases x=10Sample proportion p^=x/n=10/42=0.2381

Q: The equation below estimates the effect of race on the probability of mortgage denial, holding…

A: Given that,      Pr(deny=1|P/I ratio, black)=(-2.29 + 2.78 P/I ratio+ 0.71 black)where,      is the…

Q: A diagnostic test for a certain disease is applied to n individuals known to not have the disease.…

A: Let X= the number among the n test results that are positive.X is the number of false positives).…

Q: The average time it takes a salesperson to finish a sale on the phone is 9 minutes and is…

A: 2c) According to the given information,Mean, μ = 9 minutes.Let X be a random variable represents the…

Q: 21. 2400 voters were polled regarding ballot measure 95. The voters were separated by party -…

A: It is required to identify the particular party, being a member of which, is independent of…

Q: A recent study evaluated how addicted teenagers become to nicotine once they start smoking. The…

A: The female teenagers, The mean HONC score for females, The mean HONC score for males, The male…

Q: Prove that: o²x = E {X²} - [E{X}]² = M2 - M1²

A:

Q: 3.1 Repeat observing a distance for n times with independent equal weight. Please proof that the…

A: To prove that the most probable value (MPV) of the observations is the direct mean by the Least…

Q: A Gamma random variable has mean of 5.4 and variance of 16.2. Find the parameters of this…

A: The mean of a Gamma distribution is The variance of a Gamma distribution is

Q: What is the probability of a spinner with 5 even colors landing on the same color 4 or fewer times…

A:

Q: The population mean and standard deviation are given below. Find the required probability and…

A: sample size(n)=75Mean()=223standard deviation()=5.9

Q: 2. Suppose X and Y each have an exponential distribution with parameter a, find the joint p.d.f of X…

A: Suppose X and Y each have an exponential distribution with parameter .

Q: D. The Swiss embassy has 65 employees. Of these employees, 47 speak German, 35 Speak Italian, and 20…

A: Given,Total employees = 65Number of employees speak German, n(G) = 47Number of employees speak…

Q: Certain birth defects and syndromes are polygenetic in nature.​ Typically, the chance that an…

A: Let the following events be defined as:A : A child is born with affliction AA1: The first child born…

Q: 3. A Poisson random variable X has standard deviation σX = 3. What is the probability that X = 2?…

A: HereStandard deviation σ=3

Q: Brandy is sorting through her many pairs of socks, and is counting how many of each color she has.…

A: The number of white pairs of socks is 48. The number of black pairs of socks is 52. The number of…

Q: A uniform random variable X has a probability density given by: 1/0≤x≤2 otherwise f(x) = The mean of…

A: Mean=1, variance=13

Q: Consider two random variables X and Y with the following joint density function f(x,y) = {e^** a)…

A: f(x,y)=e−x;0≤y≤x&lt;∞

Q: If the PDF of X is f(x)=2x/k2 for 0<x<k, for what value of k is the variance of X equal to 2?

A: The probability density function of Xf(x)=2x/k2      for 0&lt;x&lt;kfor what value of k the…

Q: for part ii) why was for the probability of 6 or more incidents in one month, 0.12 and 015 used? is…

A: ii) Using the given table, the probability of there was atleast 6 safety incidents per month is…

Q: Find the z-score that has 12.1% of the distribution's area to its left. The Z-score is. (Round to…

A: From the provided information,12.1% of the distribution's area to its left.

Q: The time between accidents at a busy intersection has a Exponential distribution with mean of 0.2…

A: Mean=0.2x~Exponential()F(x)=P(Xx)=

Q: P(X ≤ 1 and Y≤ 1) = 0.41 (c) Give a word description of the event {X = 0 and Y# 0}. At most one hose…

A: Let X and Y have a joint pmf

Q: Candidate A and Candidate B have a hotly contested race for Florida's electoral votes. Suppose each…

A: P=0.5003We have 8084000 voters in Florida

Q: Consider the following Venn Diagram, depicting the data from a survey of college students who may…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: P 1) a) Find the value of zo such that P(Z > %o) = 0.5. ERN b) Find the value of zo such that P(Z…

A: (a) P(Z&gt;Zo)=0.5(b)P(Z &lt;Zo)=0.8643(c)P(−Zo &lt;Z &lt;Zo)=0.90

Q: please answer this question

A: We have to findV(X)=1λ2