Choose points from (0, 1) uniformly and add the numbers together. Stop this process when your add is greater than one. Let N be the random variable which is the number of points that you selected. Find E(N).

Q: If the random variable X follows N (0, 2) and Y = 3X, find the mean and vari- %3D ance of Y.

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Q: For two random variables X and Y where X∼ exponential(0.5) and Y|X = x ∼ N(5,x2), find E(E(X|Y ))

A: Given, Two random variables X and Y such that X~Exp(0.5) and Y|X=x ~N(5,x2)

Q: Let X be a random variable that takes on values between 0 and c. That is, P(0 < X < c) = 1. Show…

A: Solution-: Given that x be the continuous random variable that takes values  between 0  and c i.e.…

Q: Let X be a random variable with the function, Let f(x) = {0*(1 – 0)*forx = 0,1, elsewhere. Assume T1…

A: T1  = mean of X1  = summation (X*f(x)) = 0*f(0)+ 1*f(1) = f(1)= (theta)(1-theta)

Q: The hits to a Web site occur at the rate of 12 per minute between 7:00 P.M. and 11:00 P.M. The…

A: Solution: The random variable X is defined as the number of hits to the Web site between 7.13 P.M.…

Q: Let X be a random variable representing a risk with E(X) = 10 and E(X2) = 125. %3D A portfolio…

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Q: Decide whether the random variable x is discrete or continuous. x represents the length of time it…

A: We know that discrete variables take a finite number of countable points whereas a continuous random…

Q: for r, y > 0, f(x, y) = (1+x)2.(1+xy)² > 0, otherwise. Show that X and X Y are independent,…

A: *answer:

Q: Let the random variable X fit uniformly in the interval (-1,1). Find the distribution of the random…

A: Given: The random variable X follows a uniform distribution in the interval (-1,1). Let Y=X2…

Q: Let Y1 and Y2 be independent random variables that are both uniformly distributed on the interval…

A: Consider that Y1 and Y2 are two continuous real valued random variables with joint probability…

Q: Xenia has a bag which contains 5 red marbles and 4 pink marbles. She draws marbles one at a time…

A: Given Red marbles Pink marbles 5 4 R→random variable which counts the 'number of red…

Q: For N random variables, show that, (W,t..un) Px1..... <Ox1. x, (0,.0) =1 .......

A: Answer: For the given data,

Q: Let X1, X2,..., Xn ~ N(μ, 0²) independent random variables. Find the distribution X+X2+…+Xn X= = n…

A: Given Xi~N(μ, σ2) be the iid and i=1,2,...,n  Result: X and Y are independent then E(XY)=E(X)E(Y)…

Q: X and Y are random variables such that Var(X) = 4, Var(Y) = 6 and Var(X+Y) = 16. Calculate Var(a X +…

A: We want to find V(aX+bY)= ?

Q: Let us say that we have jointly distributed random variables X and Y with E(X) = 3, E(Y) = 5, Var…

A:

Q: Let X and Y be two random variable with E(X) = 1,Var(X) = 2, E(Y) = 2,Var(Y) = 2. Then Cov(X –…

A: GivenE(x)=1Var(x)=2E(y)=2Var(y)=2

Q: Let X and Y are two independent random variables with probabilities P(X) = {0.25,0.45,0.3} and P(Y)…

A:

Q: Find the range for each of the following random variables. 1. I toss a coin 100 times. Let X be the…

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Q: Let X1, X2, ., Xx, be a random sample from N(0,0), find a C.S.S for 0.

A: Note: According to our guidelines we solve only the first question if multiple questions are posted.…

Q: Find the Mean of f(x), where f(x) = 6X+6. The probability distribution of a random variable X ; if X…

A: Mean is an average value around which the whole data set is concentrated.…

Q: Let X and Y be Bernoulli random variables. Let Z = X + Y. a) Show that if X and Y cannot both be…

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Q: Let X be a random variable taking only the values 0, 1, 2, 3, 4 with probabilities given by P(X = 0)…

A: Discrete probabilty  The conditions of the probability is 1) p(x) ≥ 0 2) Σp(x)=1

Q: The numbers x and y are chosen at random from a circle of radius 6. What is the probability that x +…

A: Probability = Area under interest/ total area Where Area under interest = shaded area Total area =…

Q: what is E[XY]?

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Q: The discrete random variable X has the probability function, where k is canstant kx x=2,4,6,8, 10 f…

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Q: Show that the random variables X and Y are not independent and find P(X = 0|Y_ 2), P(X = 1|Y = 2),…

A: For the independence of two variables, we must have P(X = x, Y = y) = P(X = x).P(Y=y)

Q: Let X1, ... , X49 be a random sample of 49 independent and identically distributed uniform…

A: Given that X1,X2,....X49 be a random sample of 49 independent and identically distributed uniform…

Q: Consider random variable X whose CDF is given as follows -1 (a) Let Y = X2. Then find CDF and PDF of…

A: ...

Q: If X,XXy and Y, Y Y spectively, then the distribution of 2X-F is: are two random samples that…

A: Given that Xi~N0,4 and Yi~N0,25 n1=25, n2=16

Q: Let X be Poisson random variable with the mean λ. Find the value of λ that satisfies P(X = 0|X ≤ 2)…

A: Let X be a random variable which follows Poisson distribution with a population mean λ. X~P(λ) The…

Q: Z,, Z2, .. is a random sample of N(0,1), find the ution of Y = E,(2, – 2)²

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Q: Xenia has a bag which contains 5 red marbles and 4 pink marbles. She draws marbles one at a time…

A: Bag contains 9 marbles of which 5 are red and 4 are pink. The experiment consisting of drawing one…

Q: Let X and Y be binomial random variables with distributions of Bi(n, p) and Bi(m, p) respectively.…

A: It is given that the probability generating function of X is, The probability generating function…

Q: Show that if X and Y are independent Exp(a)-distributed random vari- ables, then X/Y e F(2, 2).

A: The distribution of a continuous random variable can be identified by its pdf because the pdf of…

Q: If the random Variable x has a uniform distribution the interval [0,5] on Find P(2<XS4).

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Q: Find the distribution of Z X+Y, if X and Y are jointly continuous random variables F given by

A: Given information: The joint probability density function of the random variables X and Y is given.

Q: the random variable Y is such that : E(2Y+3)=6    and    Var(2-3Y)=11 find      E(Y^2)

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Q: The cdf of a continuous random variable X is given. Find P(2.4<X<6.1). if x s2 F(x) = 0.2x -0.4 if…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: X and Y are independent random variables uniformly distributed over (0, 1). Compute the probability…

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Q: hat is its skew?

A: Given that, A random variable is uniformly distributed over [0,1].

Q: Let X and Y be two independent random variables distributed uniformly on the interval [0, 1]. What…

A:

Q: Find P(XS3) if the cumulative distribution function for the random variable X is: 0, x<-1, 0.25,…

A: From the given information, let X be a random variable having the cumulative distribution function…

Q: Determine the distribution of the random variable X and sketch its graph. for x € (-00, -1) for r€…

A: We want to find random variable and sketch the graph.

Q: The continuous random variable X is uniformly distributed over the interval [2.5, 3.5|].

A:

Q: Let X1, X2, ..., Xn be independent and identically distributed random variables, X ∼ Exp(λ). Show…

A: Given  X1, X2, ..., Xn be independent and identically distributed random variables X ∼ Exp(λ) The…

Q: Let X and Y be independent random variables distributed as N(-1, 1) and N(1, 1), respectively. Find…

A: Given: X follows a  normal distribution with mean -1 i.e. µ= -1 and the standard deviation of 1 i.e.…

Q: The random variable V has a PMF of PV(v) of c(1/2)n when n = 0, 1, 2, 3 and it is 0 otherwise. Set…

A: The function is PMF if ∑Pi=1 so it follows: c120+c121+c122+c123=1c1+12+14+18=1c158=1c=815 Hence the…

Q: Let X be a random variable with p.d.f f(x) =x(9-x), 0sxS 3. Find the mode.

A: Introduction Mode: Mode is one of the types of measures of central tendency. Mode is the location…

Q: X has been defined as the Poisson random variable. Thus, P (X = 1) = 0.149 and P (X = 2) = 0.224 are…

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Q: Suppose a random variable Y uniformly distributed over the interval [2, 7]. 1. What is f(y)?

A: It is given that Y follows Uniform(a = 2, b = 7) To find : The probability density function of Y.