Mx(t)=ebt-eat/t(b-a) Calculate the expected value and variance of the random variable X using the moment generating function.

Q: X is a discrete random variable and takes the values 0,1 and 2 with probabilities of 1/6, 1/3 and…

A: Moment generating function:

Q: The probability function of the random variable X is defined as f(x)=cx²(1-x)² for 0<x<1, otherwise…

A: Given information: The probability distribution function of the random variable X is defined as:…

Q: 2- Three alternative rice production technologies have returns that are approximately normally…

A: Given :

Q: 7. A pumping station operator observes that the demand for water at a certain hour of the day can be…

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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?

Q: Let X be a continuous random variable with PDF 2x fx\=) = { otherwise Find the expected value of X.

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Q: Example 3: If a random variable X has the moment generating function is given by M(t) = 2 find the…

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Q: Example 3 : If a random variable X has the moment generating function is given by find the variance…

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Q: The Bernoulli Process Strictly speaking, the Bernoulli process must possess the following…

A: Given that  the Bernoulli process must possess the following properties:   1. The experiment…

Q: Ben throws a dart at a circular target of radius r. We assume that he always hits the target, and…

A: Radius of given circle is: r Here we can find the two conditions when he throws the dart on…

Q: 3. Let the lifetime of a stochastic status model have underlying survival function V100-x Sx (x) =-…

A: The survival function is Sxx=100-x10 The probability that the person survives from 43 to 50 but does…

Q: X³, 2Y²-3Y+4)  Calculate the covariance by creating a common distribution table for the given…

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Q: b. Find E[X(X – 1)] for Poisson random variable. Use the result to find the variance of X.

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Q: (X³ , 2Y²-3Y+4)  Calculate the covariance by creating a common distribution table for the given…

A: Given : (X³ , 2 Y²-3 Y+4)

Q: The marginal distributions of two random variables X and Y, together with some values of their joint…

A: Solution-: We have following table:   Y=1 Y=2 Y=3 Total X=1 - 0.21 - 0.7 X=2 - 0.09 - 0.3…

Q: A +Y. (ii) Let X and Y be independent poisson random variables with respective parameters A and A…

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Q: If y,y2y be a random sample taken from a Poisson distribution with parameter 2, then the…

A: Given that Y1, Y2,…Ym is a random sample from a Poisson distribution with parameter λ. The PDF is…

Q: Let X be a discrete random variable with moment generating function 1 M(t) (e² + e=t) (e² + e³t +…

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Q: 3. Let the lifetime of a stochastic status model have underlying survival function V100-x Sx (x)=-…

A: Solution: Given that, Survival function is                                  Sx(x)=100-x10…

Q: fx(x)={12/11(1−x2) −1/2≤x≤1/2 0 otherwise Random…

A: Consider the provided function, fxx=12111-x2,      -12≤x≤120,                         otherwise…

Q: * The likelihood function of the random sample Xi-Binomial(3,0), with (x1,x2,x3,x4)%3D(1,3,2.2) is

A: Given : Xi follows Binomial distribution with n = 3 and parameter theta.  Random sample of size 4…

Q: 1. Find the second-order prediction error filter and the prediction error variance for the random…

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Q: A milk man buys milk at K10 per litre and sells it at K12 if sold on the same day; if not, it can be…

A: Let 'X' be the random variable representing the demand for milk per day.  X~Ua=45, b=60 The demand…

Q: he dummy variables in a model of human capital can be used to: Select one: a. None of these b.…

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Q: Get the moment-generating function and based on it, calculate the average and variance of X

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Q: Example 21: Let X be the random variable with probability law: P (X = r) = q-1 p; r = 1, 2, 3, ...…

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Q: Derive the expected value of Y? Suppose that a random variable Y is uniformly distributed on an…

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Q: how do I use markov's and chepyshev's inequalities to obtain bounds for the probability of having an…

A: Using Markov's Inequality: According to Markov's Inequality, if X is a non-negative random variable…

Q: fx(x) 4 a -1a

A: We have to find the value of constant for valid pdf.

Q: X∼U(a,b) , Using the moment generating function. Calculate the expected value and variance of the…

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Q: (a) Suppose rain is falling at an average rate of 30 drops per square inch per minute. What is the…

A: Hello. Since your question has multiple, we will solve first question for you. If you want remaining…

Q: In a small metropolitan area, annual losses due to storm, fire and theft are independent,…

A: Given,      A random variable X~exponentially      distributed.      with Means 1.0,1.5 and…

Q: Let Y1, . . . , YN be a random sample from the Normal distribution Yi ∼ N(ln β, s2) where s^2 is…

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Q: Find the variance of the random variable Y where 3 )2,0y < 2 fr(u) 8

A: The given that the probability density function of the random variable Y is,

Q: Let X Poisson(A) and Y = vX. Use the delta method to approximate the mean and variance of Y.

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Q: Consider the performance function Y= 2X1-2X2+8X3  are all normally distributed random variables with…

A: Given that Y=2X1-2X2+8X2 is normally distributed. Mean of Y=E(Y)= 2*10.4-2*11.8+8*11.5 E(Y)=89.2

Q: Find the stable distribution for the regular stochastic matrix.   0.5 0.2 0.3 0.4 0.7 0.7 0.1 0.1 0…

A: From the given information, Consider,

Q: a) Find the expectation E (X) of X. E(X) = 0 (b) Find the variance VarX) of X. Var(X) = 0

A: Given: x P(x) 0 0.35 10 0.35 20 0.05 30 0.25 Total 1

Q: Identify the distributions of the random variables with the moment- generating functions shown…

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Q: (iii) Find the equilibrium state probability vector ĩ.

A: Here AS PER your request I have calculated 3rd only

Q: Let X be the random variable with the cumulative probability distribution: 0 x < 0 F(x) = {₁ - e -²x…

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Q: Y1. Y2. Y, are independent random variables, and .... Y, - Poisson, mean µ,. The fitted values for a…

A: Given the independent random variables Y1, Y2, . . ., Yn and Yi~Poissonμi.

Q: A computer system queues up batch jobs and processes them on an FCFS basis. Between 2 and 5 P.M.,…

A: Given: Mean arrival rate is λ=30 service rate is given as 60 minutes/ 1.2 minutes per hour which is…

Q: A5. Give the definitions for strictly- and weakly-stationary random processes.

A: given solution:  strictly stationary random process strictly method could be a model whose…

Q: Identify the distributions of the random variables with the following moment- generating functions…

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Q: Taking expectation of a Wiener process wich is normally distrubuted with n(0,1) what is the value of…

A: Given a Wiener process which is normally distributed with N0,1.

Q: Using the mid- square method obtain the random variables using Z0= 7182 until the cycle degenerates…

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Q: forester randomly locates ten 1-square-yard sampling regions in the area, the probability that none…

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Q: distributed for both children and adults. A random sample of n1 = 11 children (9 years old) showed…

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Q: Let X and Y denote two discrete random variables taking the values in x and y respectively. The…

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Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!