Suppose Y is a random variable that follows an (a, b, 1) distribution. You are given: P = 0.2 %3D 1.45455 P6 = 1.64706 P %3D 7 Calculate the expected value of Y, EY.

Q: Two random variables have expected values E[X] = 0.6 and E[Y] = 0.2 and E[XY] = 1.2. Are X and Y…

A:

Q: For the random variable X defined by the probability function below, answer the following questions.…

A: Given: x 2 3 4 5 6 7 f(x) 0.25 0.15 0.10 0.15 0.10 0.25

Q: Let X be a continuous random variable with uniform distribution, and with A = 0.19, B = 0.37. What…

A: From the provided information, X be a continuous random variable with uniform distribution with A =…

Q: A fair die is tossed twice. The random variables X and Y are the outcomes of the first and second…

A: As a fair dice is being rolled it can be assumed that X and Y are uniformly distributed between 1…

Q: You roll a pair of dice. The random variable X is the smaller of the two values, while the random…

A: Given that the pair of dice was thrown then the outcomes will be…

Q: Find a value of the standard normal random variable z, c Solve c and d fast c. P(-Zo Szszo) =0.95 d.…

A:

Q: Find the expected value for the random variable

A:

Q: The joint probability mass function of the random variables (X, Y) is given by the followin cable.…

A: We have given joint distribution of X and Y and we have to find the var(X+Y)

Q: Suppose x is a random variable best described by a uniform probability distribution with c= 15 and d…

A: Given: X  is a random variable best described  by  Uniform  probability distribution with c= 15 and…

Q: Calculate the expected value E(X) of the given random variable X. X is the lower number when two…

A: Two dices are rolled.

Q: Question 2 et Y~ B(n = 2,p=0.5). 1. Construct the probability distribution table for Y. k P(Y = k) =…

A: Given that  Y~binomial (n,p) n=2 , p=0.5

Q: Which Is a discrete random varlable? )x = "welght of the microprocessor Inside your computer" DY =…

A: In statistics, the continuous variables are variables whose values can be given by an interval, they…

Q: Calculate the expected value E(X) for the given random variable X. Select 13 cards without…

A: From the provided information, Total cards in standard deck = 52 13 cards selected without…

Q: Z is the standard normal random variable E(Z) = 1 Var (Z) = 0.a O E(Z) = 1 Var (Z) = 1.b O E(Z) = 0…

A:

Q: let Y be a random variable that can either be equal to 0 to 1. let p(Y=1)=p,what is E(|Y-p|)?

A:

Q: The cdf of a random variable Y is |1– exp(-0.4y), y 20 F,(y) otherwise Valuate P{2.5 <Y < 6.2}.

A:

Q: vo random variables X-(-1,0) and Y=(2,3) are equiprobable and independent. Determine the

A: Given that there are two random variables. X=(-1, 0) and Y=(2, 3). Both equiprobable. That is,…

Q: Suppose x is a normally distributed random variable with u = 31 and o = 6. Find a value xo of the…

A:

Q: X1 + X1 + ...+Xn Find the characteristic function of the random variable Y =-

A:

Q: Suppose X is a random variable with the following distribution: xi 1 2 5 10 pi 0.4 0.3 0.2…

A: the expected value of X is given by the formula EX=∑ixipi substitute the values…

Q: For each match you play, your probability of winning is 2/3. You plan to play 5 matches, but if you…

A: Sol:- To calculate the expected values and variances of X and Y, we first need to analyze the…

Q: Z is the standard normal random variable E(Z) = 1 Var (Z) = 0 .a O %3D E(Z) = 1 Var (Z) = 1.b O

A: In the standardized form, the normal distribution has a mean equal to zero and standard deviation…

Q: For two random variables X and Y, the following information is given. V(X)= 3, V(Y)=2 and cov(X, Y)…

A: Given that for two random variable X and Y,  VX=3VY=2cov(X,Y)=-1   The following variance propertied…

Q: 3.12 Let Y be a random variable with p(y) given in the accompanying table. Find E(Y), E(1/Y),…

A:

Q: 3. Let X and Y be two Binary random variables with joint probability distribution: x = 0 x = 1 0.2…

A: The joint probability density function is given as- fx,y x=0 x=1 y=0 0.2 0.4 y=1 0.1 0.3

Q: 3. Find the binomial probability for each exercise below. Label each parameter as x, n, and p. Find…

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

Q: Let X and Y be two random variables and E(Y) 1. Which one of the following is true about E(Y|X)? a.…

A: Solution

Q: Hint: treat RV X[Y = y as it's own Normal RV, X, that has the conditional mean and %3D variance we…

A: Solution...

Q: Let X and Y be the two possible events of an experiment where, p(X) = 0.5, (XUY) = 0.9 and p(Y) = p.…

A:

Q: Find the expected value for the random variable: X 1 2 4 P(X) 0.21 0.25 0.11 0.43 E(X) =

A:

Q: Consider the three normal random variables Y Ν(μ-0,σ?4) , Y , Ν (μ Y3 ~ N(µ = -3, o² = 3). Find the…

A:

Q: What value of the x axis marks the top 25% of the distribution?

A: Given:  Let x be a normally distributed random variable with the following parameter: mu=125…

Q: Suppose Y1, Y2, ·…,Yn is an iid sample from a N(µ, ở) population distribution. Let Y and S? denote…

A: Find the distribution of Q12+Q2

Q: The combined probability of the random variable X and Y is given below: a. Find the value of the…

A: Given: f(x,y)=cxy0&lt;x&lt;2       o&lt;y&lt;x0otherwise (a) Value of constant c: ∫02∫0xcxy dy…

Q: If a random variable follows a Poisson distribution and if: 4P(x=0)=P(x=1), then find E(x² ) Select…

A: For a poisson distribution  EX2=λ2+λ

Q: Suppose that the PDF for the number of years it takes to earn a Bachelor of Science (B.S.) degree is…

A:

Q: Find the expected value for the random variable:     X     1       2       4       6   P(X)   0.16…

A: Given data,   E(X)=?

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!