Suppose that X is a normal random variable with mean 5.
If P(X>7) =4, approximately what is the variance of X?
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1. State three properties of the normal distribution. [3 marks) (a) Suppose that X is a normal random variable with mean 5. If P{X > 9} = 0.2, approximately what is Var(X)? - [3 marks] (b) Let Y be a normal random variable with mean 12 and variance 4. Find the value of c such that P{Y > c} = 0.10. [3 marks)
3) Suppose X is a Normal RV with mean = 17 and variance = 4. Note this is the same random variable as in Question 2. Find (a) P&717<-1.5) (b) P(-1.25 < *=12 <.5) (c) P(+297 < 2)
. Suppose that Y is a normal random variable with mean µ = 3 and variance σ 2 = 1; i.e., Y dist = N(3, 1). Also suppose that X is a binomial random variable with n = 2 and p = 1/4; i.e., X dist = Bin(2, 1/4). Suppose X and Y are independent random variables. Find the expected value of Y X. Hint: Consider conditioning on the events {X = j} for j = 0, 1, 2. 8....
6. Consider a sample X,... X, of normally distributed random variables with mean y and variance op. Let 5 be the sample variance and suppose that n = 16. What is the value of c for which p[x - SS (C2 - 1)] = 95 ? be the 7. Consider a sample X,...,X, of normally distributed random variables with variance o? = 30. Let S sample variance and suppose that n-61. What is the value of c for which P...
7. X is a random variable with a mean of 2 and a variance of 3, and Y is a random variable with a mean of 4 and a variance of 5, and the covariance between X and Y is -3. Define (a) Find the expected value of W. b) Find the variance of W
Let X be a normal random variable with mean 4 and variance 3. Find the value of c such that P{|X − 4| > c} = 0.1 please solve properly.
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Consider the normal random variable X with mean 3 and variance 4. Find the best Chernoff estimate on P(X>=5). Please do not use Z-table or Z-test. Solve only using Chernoff estimate. Thanks.
Suppose X, Y and Z are independent standard normal random variables. Then W = 2X + Y - Z is a random variable with mean 0 and variance 2, but not necessarily normal distributed. a normal random variable with mean 0 and variance 4. O a random variable with mean 0 and variance 4, but not necessarily normal distributed. a random variable with mean 0 and variance 6, but not necessarily normal distributed. a normal random variable with mean 0...
Suppose X, Y and Z are independent standard normal random variables. Then W = 2X + Y - Z is a random variable with mean 0 and variance 2, but not necessarily normal distributed. a normal random variable with mean 0 and variance 4. O a random variable with mean 0 and variance 4, but not necessarily normal distributed. a random variable with mean 0 and variance 6, but not necessarily normal distributed. a normal random variable with mean 0...