Suppose that you have a fair 4-sided die, and let X be the random variable representing the value of the number rolled. (a) Write down the moment generating function for X. (b) Use this moment generating function to compute the first and second moments of X.

Q: A fair die, with its faces numbered from 1 to 6, is one in which each number is equally likely to…

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

Q: A screening test for a disease shows a positive test result in 95% of all cases when the disease is…

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Q: d) Calculate the 2nd moment with respect to the mean of this random variable.

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Q: Q21. Define moment generating function of random variables. Show that the moment generating function…

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Q: the moment generating function of the random variable is always exist

A: The moment generating function of a random variable x, Mx(t) always exists. or not?

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A: In statistics theory, the uniform distribution is the distribution which can be defined as both…

Q: Let the random variable X assume the value r, with probability law P(X=r) =q P, Find the moment…

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Q: A factory received a shipment of 9 flanges, and the vendor who sold the items knows there are 2…

A: According to the provided information, there are 9 flanges and 2 flanges in the shipment that are…

Q: d. Let X and Y be independent normal random variables, each with mean u and standard deviation o. 1.…

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Q: A factory received a shipment of 15 capacitors, and the vendor who sold the items knows there are 8…

A: b) He can choose any 6 capacitors from 15 capacitors  in 15C6=5005 ways   He can choose 4 defective…

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Q: Let Y1, Y2, Y3 be independent binomial random variables with probability of success, p=0.4, and…

A: From the given information, Y1,Y2,Y3 be independent binomial random variables with probability of…

Q: With continuous random variables, we never calculate the probability that X has a particular…

A: The continuous random variable takes any values within two admissible values and the probability…

Q: Let X be a Poisson random variable with parameter k. (a) Show that the moment generating function…

A: Here X~ Poi(k). Then, P(X=x)=e-kkxx!,x=0,1,2,...0,otherwise a.)The Moment Generating Function of X…

Q: A factory received a shipment of 15 sprockets, and the vendor who sold the items knows there are 7…

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A: Given: Research has shown that approximately 1 woman in 700 carries a mutation of a particular gene.…

Q: A coin is tossed tl probability of get

A: Given A coin is tossed three times, Hence the sample space (s)  = ( HHH,HHT,HTH,THH,TTH,THT,HTT,TTT…

Q: Let Mx, y be the moment generating function of random variables that are not independent of X and Y.…

A: We have given that, X & Y are two random variables which are not independent.  If MX,Y(t1,t2) is…

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Q: A sample of size 200 is taken at random from an infinite population. Given that the population…

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A: It is given that, One thousand tickets are sold at 3$ each for a colour T.V valued at 350$. Then,…

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A: Total people = 467 + 376 =843

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A: Sample space (S): Total possible outcome n(S) = 8*8 = 64

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A: The probability function of X is given by X -1 1 P(x) 2/3 1/3

Q: factory received a shipment of 14 flanges, and the vendor who sold the items knows there are 7…

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Q: Refer to Exercise 3.145. Use the uniqueness of moment-generating functions to give the dis-…

A: We have given that the random variable with moment generating function  m(t) = (0.6et + 0.4)3

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A: Solution : Given that : p = 0.238n = 500mean = np            = 500 × 0.238            = 119sd =…

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Q: Suppose 40 % of students who drive to campus carry jump cables in their cars in case of a dead…

A: NOTE : As per our company guidelines, we are supposed to answer only the first 3 parts. Kindly…

Q: p is 0.2

A: Sample mean is an estimate of population mean Sample mean = (4+5+6)/3 = 5 here, population is…

Q: Use the uniqueness of moment-generating functions to give the distribution of a random variable with…

A: The uniqueness theorem states that the moment generating function uniquely defines the distribution…

Q: A factory received a shipment of 14 flanges, and the vendor who sold the items knows there are 8…

A: Solution: a. From the given information, there are 14 flanges. Out of which there are 8 flanges are…

Q: A screening test for a particular infectious disease shows a positive test result in 90% of all…

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Q: A random variable X has a N(0,1) distribution. Use the moment generating function of X to compute…

A: We have given that, X be random variable that follows standard normal distribution i.e.,…

Q: What is the entropy when the delivery is blended?

A: Decision tree

Q: The United States Department of Agriculture (USDA) found that the proportion of young adults ages…

A: Population proportion: P=0.238 Sample size= n= 500 a) To find probability that number of…

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A: Let , X has geometric distribution with parameter p=0.8 Therefore , the probability mass function of…

Q: d. Let X and Y be independent normal random variables, each with mean µ and standard deviation o. 1.…

A: 1) According to the given information, X~Nμ, σ2 Y~Nμ, σ2   For a normal random variable X, the…

Q: Example 4 Suppose that you have a fair 4-sided die, and let X be the random variable representing…

A: It is an important part of statistics. It is widely used.

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Q: Given that X has the probability distribution f(x) for a 0,1, 2,3, and 4. 16 Find the…

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Q: Let X be a random variable with probability Law P (X =r) = q-", K for r=1,2,3... 0, Find the moment…

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Q: Cal Poly Pomona found that 15% of its students withdraw without completing Calculus I course. Assume…

A: Given P(success)=0.15 q=0.85 n=30

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.