3) A discrete random variable X has the following probability distribution: 1 2 4 6. 7 P(X) K 2K 2K 3K K2 2K2 7K2+K Find the value of K. Also find the mean and variance of the distribution.

Q: 27. A discrete random variable Y has a probability distribution as follows: Y 1 2 10 15 P(Y = y) 0.2…

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Q: 1. Consider two discrete random variables, X and Y with marginal pmf's fx(x) and fy (y). Come up…

A: Consider two random variables X~Binomial(n=10, p=0.5) and Y~Poisson(lambda=5), then-…

Q: The discrete random variable X has the probability distribution 2 4 P(X=x) k 2k 3k 4k 3.

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Q: If two random variables X and Y are statistically independent, then X and Y are said to be…

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Q: 3. The expection of a random variable X is equal to 5. What can be say about the expectations of (a)…

A: Given, Expectation of random variable X is 5. E(X) =5

Q: we are evaluating two random variables X and Y with probabilitydistribution equal to: p(x, y) = P (X…

A:

Q: consider a discrete random variable Y with the following probability table. -2 3 9. 12 p(y) 0.21…

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Q: Suppose the random variable X has the following probability distribution -1 1 P(X=x) 0.2 0.3 0.3 0.2…

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Q: (1) If two random variables X and Y are statistically independent, then X and Y are said to be…

A: Given that  (1) If two random variables X and Y are statistically independent, then X and Y are said…

Q: The discrete random variable X has the following probability distribution: 2 0.2 |4 |10 P(x) 0.3…

A: Solution: From the given information, probability distribution for the discrete random variable X is

Q: 4.62 If X and Y are independent random variables with variances o of the random variable Z = -2X +…

A: Given that Var(X) = 5 And Var(Y) = 3

Q: 3. If X and Y are standardized random variables and 1 + 2ab r(aX + bY, bX + aY) a? + b? Find r(X,…

A: Reviewing information, Given X & Y are standardized variables r(aX+bY, bX+aY)=1+2aba2+b2

Q: Suppose a normally distributed random variable x has a mean of 100 and P(x < 90) = 0.30. What is the…

A: Given : Mean ,u = 100  P(x &lt; 90) = 0.30 where x = 90

Q: 4. The expected value of a random variable X is 10 and its variance is 16. If the random variable X…

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Q: 4.62 If X and Y are independent random variables with variances o = of the random variable Z = -2X +…

A: 4.62: Given that X and Y are independent random variables with variances σX2=5 and σy2=3. And σXY=0…

Q: 12: 35 If a continuous random variable x follows rectangular distribution in the range (2, 7), find…

A:

Q: If a random variable X has mean 3 and variance 4, then E(X² + 3X + 2) is

A: GivenMean=E(X)=3Variance=V(X)=4

Q: 2. Find the mean, variance and standard deviation of the probability distribution of the random…

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Q: Suppose X and Y are independent random variables with expected values E[X] = 0, E[Y] = 0, and Var(X)…

A: We have given that  X and Y are independent random variables with expected values E[X] = 0, E[Y] =…

Q: 2. The number of patients visiting an emergency room during the graveyard shift (11:00pm-7:00pm),…

A: Given probability distribution: X 0 1 2 3 4 5 6 P(X=x) 0.05 0.20 0.25 0.20 0.10 0.15 0.05

Q: Suppose that Y is a discrete random variable with mean u and variance o and let W = 5Y. (a) Do you…

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Q: If XX represents a random variable coming from a normal distribution with mean 3 and if…

A: X represents a random variable coming from a normal distribution with mean, μ=3 Since,…

Q: 2. Find the mean of the probability distribution of the random variable X which can take only the…

A: Given :P(2)=310P(3)=25P(4)=15P(5)=110

Q: 4. Given the discrete random variable X: What is the probability distribution of X if X~ B(2, )? O…

A: Given: A discrete random variable X. As X~B2, 517 so, Total number of trials(n)=2 The probability of…

Q: 13) The HR manager of a company has developed a probability distribution of the number of absent…

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Q: Since P {X = -6} = 1/6, P {X = 3} = 1/3, P {X = 4} = 1/2  , Calculate the expected value and…

A: Expected value:E(X)=∑xipi=-616+313+412=2

Q: 5. Suppose that X and Y are random variables having the joint probability distribution: 1 3 0.25…

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Q: Let X be a binomial random variable with n=7 and p=0.1, then The variance of X is 0.63 P(X>1)=…

A: Given: n=7 and p=0.1 Then, the variance isVariance=np1-p=70.11-0.1=70.10.9=0.63

Q: 8 A discrete random variable X has the following probability distribution. 2 3 4 P(X = x) 3c 4c Sc…

A: i) The total probability is always 1.  So, 3c+4c+5c+6c=1  or, 18c=1or, c=118

Q: If X is a random variable with Binomial distribution of n=35 and p=0.45, find: i. E(X) ii. Var(X)…

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Q: 4. Consider the following joint probability distribution of random variables X and Y f(x, y) = (3x –…

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Q: A discrete random variable x has the the following probability distribution      X 1 2 3 4 5…

A: Introduction: For a discrete random variable X, the probability mass function (pmf), p (x) = P (X =…

Q: The mumber students who enter a Library in an hour is a poisson random variable. and suppose that…

A:

Q: If X is a random variable with Binomial distribution of n=35 and p=0.45, find:    i. E(X) ii.…

A:

Q: 10. Consider the random variable X whose probability distribution is given below: X Pr(X = x) 1 2 2k…

A:

Q: 1. Suppose the PMF of the random variable X is px(x) = .21(1.3)(x) +.61(2)(x). What is the mean of…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: For the discrete probability distribution. 3 4. 6. 7 k 2k 2k 3k 2k2 7k + k Find the variance.

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Q: 2. If a discrete random variable X follows uniform distribution and assumes only the values 8, 9,…

A:

Q: 8. Let X be a random variable with the following probability distribution: -3 6 9 P(X=x) 1/6 1/2 1/3…

A: We have: x PX=x x1=-3 16 x2=6 12 x3=9 13 Now, the formula to calculate Ex=∑i=1nxnPX=xn…

Q: f x is a binomial random variable with n = 10 and p = 0.8, the mean value of x is _____. 8 3.2 4.8…

A: Given,If x is a binomial random variable with n = 10 and p = 0.8mean value of x=?

Q: If X represents a random variable coming from a normal distribution with mean 5 and if P(X>6.1)=0.2,…

A: Given: Meanμ=5, P(X&gt;6.1)=0.2

Q: 4. Consider the following joint probability distribution of random variables X and Y f(x,y) = (3x –…

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Q: Calculate xpectation and variance of X, if the probability distribution of the random variable X is…

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Q: 2. The number of patients visiting an emergency room during the graveyard shift (11:00pm-7:00pm),…

A: Since you have asked multiple subparts questions, we will solve first three subparts for you. To get…

Q: 1. Identify if the following scenarios describe a discrete or continuous random variable. Explain…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 1. The number of cellphones sold per day at a local cellphone shop, along with its corresponding…

A: We have given that the number of cellphones sold per day at a local cellphone shop, along with its…

Q: What is the mean of this discrete random variable? 2 3 4. 0.05 0.35 0.20 0.35 0.05 P(x)

A:

Q: 2. Find the variance and the standard deviation of the probability distribution of the random…

A: NOTE: As per the guidelines, we are supposed to solve the first question…

Q: Consider the following probability distribution for a discrete random variable X. 3 4 5 6 7 P(X=x)…

A: Given, P(X≤5.5)=?