QUESTION 2 A random variable X has probability density function f(x;0) = de Ox 0, elsewhere It is desired to test the null hypothesis H:0=1 against the alternative H₁ :0=2 0 1 A. -1.6094 Consider the test which rejects Hif X2c: 0 What will be the value of for which the level of C significance of the test is 0.1. B. 1.2223 , x>0 OC. 2.3025 OD. None of the above
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- QUESTION 10 Suppose f(x) = 1/4 over the range a ≤ x ≤ b, and suppose P(X > 4) = 1/2. What are the values for a and b? a. 2 and 6 b. Cannot answer with the information given. c. 0 and 4 d. Can be any range of x values whose length (b − a) equals 4. QUESTION 11 The probability density function, f(x), for any continuous random variable X, represents: a. all possible values that X will assume within some interval a ≤ x ≤ b. b. the probability that X takes on a specific value x. c. the height of the density function at x. d. None of these choices. QUESTION 12 Which of the following is true about f(x) when X has a uniform distribution over the interval [a, b]? a. The values of f(x) are different for various values of the random variable X. b. f(x) equals one for each possible value of X. c. f(x) equals one divided by the length of the interval from a to b.…Suppose X and Y have joint probability density function ?(x, y) = { 6x, 0 < x < 1, 0 < y < 1 − x 0, elsewhere. a. Determine whether the two random variables are dependent or independent. b. If the value of Y is 0.5, what is the probability that X will have a value greater than 0.3? Please answer this question step by step and justify your solutionLet X1, X2 .....Xn be n i.i.d. Γ(2,β) random variables where β is unknown, and the probability density function of each Xi is given by (in first screenshot) where Γ(2)=1. i) Show that the maximum likelihood estimator (MLE) βˆof β is given by βˆ = on second screenshot. ii) Now find a consistent estimator of β. Justify your answer. Γ is gamma.
- Consider the random variable with a probability density function of f(x)= (1/x ln(1.5)), 4<=x<=6 and f(x) = 0 elsewhere. What is the expected value of this random variable? What is the median of this random variable?Suppose X is a random variable taking values in the interval [0,2] with probability density function f(x) = 1-x/2. What is the variance of X?- If we assume that the moment of death of a tilapia fish in one of the commercial ponds for selling fish is Random and regular on the time period [300,0] where time is measured in minutes. So what is it Prospect 1. That the moment of death of this fish is more than three hours 2- This fish should live less than three hours 3- Find the density function, then find the expectation and variance
- ELT(Let) the joint probabilty density function of two con random variable Y and X. Please do the last three sigma x, y and PXYSuppose that the joint density function of the random variables X and Y is f(x,y)=k(1+2y), if 7<x<13 and 0<y<1, and f(x,y)=0, otherwise. Show that the marginal distribution of X is g(x)=c, if 7<x<13, and g(x)=0 otherwise. Enter the value of c. Hint: Of course, first, you need to find the value of k. Round your answer to a number with two decimal digits after the decimal point. For example if your answer is 1/40, which is equal to 0.025, then you should enter 0.03. (Do NOT use decimal comma; 0,03 would be wrong.)Suppose there is a random variable X whose probability density function has the form (shown in image). a) Find P(X>-0.2) b) Find the 90th percentile
- Question 17 If X is a random variable with the probability density function: f (x) = c|x|, for - 1 < x < 1 and 0 otherwise. What is the value of c? Please round your result to one decimal place. Correct Answer:_______________________Suppose that the random variable B has the standard normal density. What is the conditional probability density function of the sum of the two roots of the quadratic equation x2 + 2Bx + 1 = 0 given that the two roots are real? KINDLY REQUEST YOU TO PROVIDE ME WITH COMPLETE SOLUTIONQuestion 1.2 Consider the function f (x) = (1/24(x^2 +1) 1 < or = x < or = 4) = (0 otherwise) Calculate P (x = 3) Calculate P (2 < or = x < or = 3) Question 1.3 Consider the function f (x) = (k - x/4 1 < or = x < or = 3) = (0 otherwise) which is being used as a probability density function for a continuous random variable x? a. Find the value of K b. Find P (x < or = 2.5)