1. Verify whether the following functions can be considered as probability mass functions: (i) P(x = x) = x² + 1 18 (iii) P(X= x) = -, x = 0, 1, 2, 3 (1) P(X-x) = x²-2, x=1,2 (ii) 3 8 2x + 1 18 1, -, x = 0, 1, 2, 3 [Ans.: Yes) [Ans.: No] [Ans.: No]
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![1. Verify whether the following functions can be considered as probability
mass functions:
(i) P(x = x) =
x² + 1
18
(iii) P(X= x) =
-, x = 0, 1, 2, 3
(ii) P(X - x) - ²-2,
-, x= 1, 2, 3
2x + 1
18
-, x = 0, 1, 2, 3
[Ans.: Yes)
[Ans.: No]
[Ans.: No]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F319cd0db-f741-4e7e-91cf-8017f925f00c%2Ff685966a-12cc-4b9e-8dc3-ec1cb4b05cbf%2F0fdpvhs_processed.jpeg&w=3840&q=75)
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- . Determine the value for c and the covariance and correlation for the joint probability mass function fXY (x, y ) = c (x + y) for x = 75, 75+1, 75+2 and y = 75, 75+1, 75+2. (Round up after multiplying) (Sum of probabilities = ?)Solve c,d9. Consider the formula: P(x) = x/21, x 0, 1, 2, 4. Is P(x) a probability mass function? If so, show the distribution of X in tabular form and compute the expected value of X.
- Show that if t" (t + t) where t and ť are both most efficient estimators with variance v, then var (t") = v (1 + p).Q. 4 Let X and Y be two continuous random variables with following joint probability density function SK (x² + y²); 0 Y), (c) P(X +Y > 1) (b)If the joint probability distribution of X and Y is given by * x+y f(x,y) = for x = 30 0,1,2,3; y = 0,1,2. Find the marginal distribution of Y X f(x, y) 1 2 3 1 2 3 30 30 2 30 4 1 Y 30 2 30 3 30 4 30 2 30 30 30 30 Y 1 2 y 1 2 f(y) 1 1 3 f(y) 1 7 10 10 5 3 15 If none of the choices, fill the table Y 1 2 | 0 |1 |2 | 3 f(y) 1 3 f(x) - 10 3 15
- Two discrete random variables X and Y have joint probability mass function (pmf) (a) (b) (c) ƒ(x) = { 5 0 Calculate the value of k. Show that f(x|y) Show that f(y x) = k n(n+1) = 1 n 1 8 x = 1,2,..., n; y=1,2,...,x. otherwise. The probability that a newborn life (age 0) survives x years is given by: 110 - x xPo 04. Let X be a positive random variable (i.e. P(X 1/E(X) (b) E(-log(X)) > -log(E(X)) (c) E(log(1/X))> log(1/E(X)) (d) E(X³) > (E(X))³4. An insurance company sells an automobile policy with a deductible of one unit. Let X be the amount of the loss having pmf 0.9 f(x) = x = 0 x = 1,2,3,4,5,6 where c is a constant. a) Find c. b) Find the expected value of the amount the insurance company must pay.6. Suppose that the random variables X and Y have joint probability density function given by x+y, 0If pdf of a random variable is given by fx(x) = e* for x20 find My(v), m, and m,. XRecommended textbooks for youAdvanced Engineering MathematicsAdvanced MathISBN:9780470458365Author:Erwin KreyszigPublisher:Wiley, John & Sons, Incorporated
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