2. Suppose X has the normal distribution with parameters u and o2, fin the E(e2X).

Q: Suppose that the time X between two phone calls to a travel agency is an exponential random variable…

A: Given,A random variable X ~exponential (λ=1.5)f(x)=1.5e-1.5x  ; x≥0

Q: Suppose that x has a beta distribution with parameters a = 2.5 and B = 1. Determine to 4 decimal…

A: Given X has a beta distribution having parameters α =2.5 and β=1 So, the distribution of X can be…

Q: Suppose you have a sample of size n for variables X and Y. The sample covariance of X and Y is…

A:

Q: 5) If X has a normal distribution with mean 1 and variance 4, the P(X²-2X<8)=?

A: Given data: If X has a normal distribution  mean=  1 and variance = 4 To find; P(X²-2X&lt;8)=?

Q: X is a Gaussian random variable with the mean value of 10a and the standard deviation of 4a. a) P(a…

A:

Q: Suppose X is a random variable with normal distribution. E(X)=1 and Var(X)=4 Suppose P(X<k)=0.9773…

A: The random variable X follows normal distribution with mean 1 and variance 4. Then the standard…

Q: What are the circumstances that motivated W.S Gosset to formulate t-distribution?

A: t-distribution :  t=x-usn~tn-1 t-distribution is used when sample size is small and parent…

Q: 0, If X has a normal distribution with mean u=18 and o = 3 find a) P(16 sXS 20)

A:

Q: If X has a normal distribution with mean µ = 11 and variance σ2  = 16, find the value of x if P (X…

A: It is given that, X~ N (11, 16).

Q: 2 If x is normally distributed with a mean of 5 and standard deviation of 2, find the P(x>8).

A: Given X is normal distribution Mean = 5 Standard deviation = 2

Q: 3.139 In the daily production of a certain kind of rope, the number of defects per foot Y is assumed…

A: Here are some properties of expectation of a random variable. We will make use of these properties…

Q: Suppose that the random variable X has a lognormal distribution with parameters - = 0 and w? = 4.…

A:

Q: Suppose that f (x) = e-* for 0 < x Determine the mean and variance of the random variable.

A: Given problem Given that   Suppose that  f(x) = e-x for 0 &lt; x  The mean and variance of the…

Q: If E denotes the expectation the variance of a random variable X is denoted as

A: Here use mean and Variance of random variable X

Q: Suppose that the random variable X has mean u and variance o >0. What are the values of a and b>0…

A: Given data: The given expression is Y=a+bX. The given mean is μ=0. The given variance is…

Q: 3. Suppose that X has a Poisson distribution with h = 80. Find the probability PCX< 70) based on the…

A: Given: X has a Poisson distribution with h = 80.

Q: If X is a random variable that has a normal distribution with mean u,=10 and variance ơ,=9, Find A…

A:

Q: Let x be a continuous random variable that has a normal distribution with a mean of 50 and a…

A:

Q: Given that the variances of random variables X and Y are 1600 and 900, respectively. The correlation…

A: Variance of a Random Variable: The variance of a random variable X, denoted by Var(X), is defined as…

Q: 3. Suppose that X has a Poisson distribution with h = 80. Find the probability RCX< 70) based on the…

A: Given that, h= 80  It means that  Mean= 80 which is greater than 10. So normal approximation is…

Q: Suppose tlhe random variable X has mean p and variance o? > 0. What are the vn'ues of the numbers a…

A:

Q: Suppose that X, the height in m of adult male has normal distribution with mean 1.7m and standard…

A: It is given that the mean is 1.7 and the standard deviation is 0.2.

Q: 31) The probability that a Poisson variate X takes a positive value is 1 - e-1.5. Find the variance…

A: Given:X variable follows poisson distribution.Find:Varaince and Probability that lies between -1.5…

Q: Suppose that the length of long-distance phone calls, measured in minutes, is known to have an…

A: Note: Since you have posted a question with multiple subparts, we will solve the first three…

Q: Find the mean and variance from the m. g.f.of binomial distribution.

A:

Q: 30. If e1+81' is the moment generating function of a normal variate X, find P(-1< X <9).

A:

Q: Given that the variances of random variables X and Y are 1600 and 400, respectively. The correlation…

A:

Q: 7. Suppose that X has a discrete uniform distribution on the integers 0 through 5. Determine the…

A: X has a discrete uniform distribution, P(X = x) = 1/N : x = 0,1,2,3,4,5 N = 5

Q: If X is normal with mean 9 and variance o? where P(X >7.5) = 0.7734 Then standard deviation of X is

A: The mean of the data is 9. The probability of event is more than 7.5 is 0.7734

Q: 3. A population of scores forms a normal distribution with a mean of µ = 50 and a standard deviațion…

A: Given that, M=44,μ=50,σ=12,n=9 The mean and standard deviation of the sampling distribution of…

Q: Suppose that x has a beta distribution with parameters a = 2.8 and B = 1. Determine to 4 decimal…

A:

Q: 27. The normal approximation to the Poisson distribution X with mean is A X~N() B X- N() cN() D X~…

A: Provided information is, the random variable is X follows poisson distribution with mean 1/4. For…

Q: Let X. XK, be a random sample of sire n from a normal distribution with population mean -0 and…

A:

Q: Suppose that x has a beta distribution with parameters a = 2.8 and B = 1. Determine to 4 decimal…

A:

Q: Suppose X1, .., Xn, for n > 1, are sampled independently from a distribution with mean u and…

A: a. From the given information, EXi=μVXi=σ2 a. Consider, EX1=μEX1+Xn2=12EX1+EXn…

Q: 3. Suppose that X has a Poisson distribution with h= 80. Find the probability PCX< 70) based on the…

A: Here use normal approximation with continuity correction factor

Q: 2. Suppose the PMF of the random variable X is px(x) =p(1-p)*(0,1...(x) where p is a constant…

A:

Q: 4) Suppose an x distribution with u = 12 and standard deviation 6. Consider two i distributions, the…

A: Given data,μ=12σ=6First based on sample size n=36Second based on sample size n=64

Q: 31. If X is a normal variate with mean 2 and S.D 3, find the -1a Also find p Y 2 distribution of Y =…

A:

Q: 3. Suppose that X has a Poisson distribution with h = 80. Find the probability P(X< 70) based on the…

A: Here when we use normal approximation we add 0.5 as continuity correction factor in X

Q: 2. Suppose a random variable X has the following distribution: 2 10 f(x) 0.2 0.2 0.5 0.1 a) Compute…

A:

Q: Suppose that X, X2,... ,X, are an iid sample from the distribution given below, f(X)e = (1/2)(1+…

A: suppose that  x1,x2....xn  are an iid sample from the distribution f(x)θ=1+xθ2 ; -1 &lt;x&lt;1…

Q: Suppose x is a normally distributed random variable with mean u =0 and standard deviation o = 1.…

A: We'll use formula here and using table we will find the value here . and after that convert that…

Q: If X has the Beta distribution with parameters a and ß, what is the probability that X equals .50

A: Given that X follows Beta(α, β)

Q: Given that the variances of random variables X and Y are 1600 and 900, respectively. The correlation…

A: The following is the formulae for Var (X + Y)                               Var (X + Y) = Var (X) +…