2. Let X be a normal random variance with media 1 and variance 4. Consider a...

2. Let X be a normal random variance with media 1 and variance 4. Consider a new variance A random variable T defined below: T = -1 if X < -2 T = 0 if - 2 ≤ X ≤ 0 T = 1 if x>0 Find the moment generating function of T and, from it, calculate E (T) and Var (T).

Expert Solution

Answer:-

orchestra answered 1 year ago

2. Let X be a normal random variance with media 1 and variance 4. Consider a...

2. Let X be a normal random variance with media 1 and variance 4. Consider a new variance A random variable T defined below: T = -1 if X < -2 T = 0 if - 2 ≤ X ≤ 0 T = 1 if x>0 Find the moment generating function of T and, from it, calculate E (T) and Var (T).

Let the random variable X is normal with mean zero and unit variance . Find the...

Let the random variable X is normal with mean zero and unit variance . Find the values of A and B such that P(A<X<B)=0.998. A= B=

1) Consider X a normal random variable with mean 4 and standard deviation 2. Given that...

1) Consider X a normal random variable with mean 4 and standard deviation 2. Given that P(X<6)=0.841345 , compute P(2<= x <= 6) 2)Consider X a normal random variable with mean 10 and standard deviation 4. Given that P(x>9)=0.598708 and P(x<12)=0.691464 . Compute P(8< x < 11).

Let ?1,?2, ?3, … , ?25, be a random sample from a normal distribution having variance...

Let ?1,?2, ?3, … , ?25, be a random sample from a normal distribution having variance 100. a. Find the rejection region for a test at level ? = .1 of ?0: ? = 0 ?1: ? = 1.5 b. What is the power of the test?

Let X have Normal distribution with mean 45 and variance 81. If a random sample of...

Let X have Normal distribution with mean 45 and variance 81. If a random sample of size 25 is taken, which of the following is the probability that the sample average is between 41.40 and 45.63?

Let X, Y, and Z independent random variables with variance 4 and mean 1. Find the...

Let X, Y, and Z independent random variables with variance 4 and mean 1. Find the correlation coefficient between (X-2YX+1) and (4X+Y)

a)Suppose random variable X has variance 1, Y has variance 4 and the variance of X...

a)Suppose random variable X has variance 1, Y has variance 4 and the variance of X + Y is 6. Which one of the statements below is correct? Group of answer choices Random variables X and Y are positively correlated Random variables X and Y are not correlated Random variables X and Y are negatively correlated Random variables X and Y are independent b)Suppose random variable X has variance 4, Y has variance 1 and the variance of X +...

Let X be a random variable which follows normal distribution with mean 12 and variance 0.25....

Let X be a random variable which follows normal distribution with mean 12 and variance 0.25. Then find the following probabilities (a) P( X ≤ 15 ) (b) P( X ≤ 17.5 ) (c) P( |X-15| ≤ 3 )

1. Let X be a random variable with mean μ and variance σ . For a...

1. Let X be a random variable with mean μ and variance σ . For a ∈ R, consider the expectation E ((X − a)2) a) Write E((X −a)2) in terms of a,μ and σ2 b) For which value a is E ((X − a)2) minimal? c) For the value a from part (b), what is E ((X − a)2)? 2. Suppose I have a group containing the following first- and second-year university students from various countries. The first 3...

2. Let Y = X^2+ X+1. (a) Evaluate the mean and variance of Y, if X...

2. Let Y = X^2+ X+1. (a) Evaluate the mean and variance of Y, if X is an exponential random variable. (b) Evaluate the mean and variance of Y, if X is a Gaussian random variable

Question

2. Let X be a normal random variance with media 1 and variance 4. Consider a...

Solutions

Expert Solution

Related Solutions

2. Let X be a normal random variance with media 1 and variance 4. Consider a...

Let the random variable X is normal with mean zero and unit variance . Find the...

1) Consider X a normal random variable with mean 4 and standard deviation 2. Given that...

Let ?1,?2, ?3, … , ?25, be a random sample from a normal distribution having variance...

Let X have Normal distribution with mean 45 and variance 81. If a random sample of...

Let X, Y, and Z independent random variables with variance 4 and mean 1. Find the...

a)Suppose random variable X has variance 1, Y has variance 4 and the variance of X...

Let X be a random variable which follows normal distribution with mean 12 and variance 0.25....

1. Let X be a random variable with mean μ and variance σ . For a...

2. Let Y = X^2+ X+1. (a) Evaluate the mean and variance of Y, if X...