(a) c (b) E[X] (c) E[X²]
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![Problem 3.3: The joint probability distribution of the discrete variables X
and Y is expressed in the table below. Find:
(a) c
(b) E[X]
(c) E[X²]
(d) E[Y]
(e) E[Y²]
(f) E[XY]
(g) E[X/Y]
(h) Var (X)
(i) Var(Y)
T
f(x,y) 1.5 2.1 2.7 3.3
0.46 0.088 0.031 0.073 0.021
0.86 0.057 0.066 0.085 0.022
1.26 0.084 0.065 0.096 0.030
1.66 0.036 0.073 C 0.089
(j) Cov(X, Y)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faca4bd6f-f1a5-495f-b05a-542e8fdd3b85%2F05cc2c7d-07e2-4bb4-b8f8-e6feebc18c73%2Fmatcck_processed.jpeg&w=3840&q=75)
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- J 1 Problem 126. Let X and Y be discrete random variables with joint probability mass function pX,Y (x, y) = C/[(x + y − 1)(x + y)(x + y + 1)], x, y = 1, 2, 3, . . . Determine the marginal mass functions of X and YProblem 1. A continuous random variable X is defined by f(x)=(3+x)^2/16 -3 ≤ x ≤ -1 =(6-2x^2)/16 -1 ≤ x ≤ 1 =(3-x^2)/16 -1 ≤ x ≤ 3 a)Verify that f(x) is density. b)Find the MeanProblem 3: Let X be the discrete random variable with the following probability mass function: x 0 1 2 3 f (x) 0.5 0.3 0.1 0.1 Find the value of the cumulative distribution function F(2).
- Problem 1: The joint probability mass function of X and Y, p(x,y), is given by: p(1, 1) = 1 9 p(2, 1) = 1 3 p(3, 1) = 1 9 (1) p(1, 2) = 1 9 p(2, 2) = 0 p(3, 2) = 1 18 (2) p(1, 3) = 0 p(2, 3) = 1 6 p(3, 3) = 1 9 (3) (4) Compute E[X|Y = i] for i = 1,2,3.Problem 4. Let Φ be the standard distribution function. Show that Φ(B(t)) / √ T − t is a martingale for 0 ≤ t < T using Itô-formula. please use definition and reasons while solving the problem.QUESTION 12 If an experiment with a random outcome is repeated a LARGE OR SMALLL number of times, the empirical probability of an event is likely to be close to the true probability due to the THE LAW OF LARGE NUMBER OR THE CENTRAL LIMIT THEOREM
- Suppose that X is an exponential random variable with mean 5. (The cumulative distribution function is F(x) = 1- e-x/5 for x >= 0, and F(x) = 0 for x < 0. (a) Compute P(X > 5). (b) Compute P(1.4 <= X <= 4.2). (c) Compute P(1.4 < X < 4.2).If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?Consider a function F (x ) = 0, if x < 0 F (x ) = 1 − e^(−x) , if x ≥ 0 Is the corresponding random variable continuous?
- Question 23: The National Institute of Mental Health published an article stating that in any one-year period, approximately 9% of American adults suffer from depression or a depressive illness. Suppose that in a survey of 2000 people in a certain city, 10% of them suffered from depression or a depressive illness. Conduct a hypothesis test to determine if the true proportion of people in that city suffering from depression or a depressive illness is more than the 9% in the general adult American population. Test the relevant hypotheses using a 10% level of significance. Give answer to at least 4 decimal places. What are the correct hypotheses? (Select the correct symbols and use decimal values not percentages.) H0: H1: Based on the hypotheses, find the following: Test Statistic = p-value = Based on the above we choose to The correct summary would be: that the true proportion of people in that city suffering from depression or a…1..Consider that a game involves the spinning of a dial which is not fair. As the dial is not fair, after spinning it is more likely to point in any particular direction than another. Suppose that the movement of a dial, X, can be modelled by the following probabilityfunction f(x) = A sin x; 0 ≤ x ≤ π. (i) Determine the value of A so that f(x) is a pdf (ii) Calculate E(X) and Var(X).If a probability generating function of a random variable x is Px(s)=(1/3+2/3s)^6 determine E(x),var(2x) and pr(X>1)
