The function f(x) = 7x for x = 1,2,4 and zero otherwise, is a probability mass function.
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Q: p(1, 1) = 0.25 p(2, 1) = 0.1 p(3, 1) = 0.1 P(XY = 2) P( \ > 1) = p(1, 2) = 0.05 p(2, 2) = 0.15 p(3,…
A: Let X and Y have joint pmf
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- Determine the value of c that makes the function f(x, y) = c(x + y) a joint probability mass function over the nine points with x = 1,2,3 and y = 1,2,3. Give exact answer in form of fraction.Suppose that p(x, y), the joint probability mass function of X and Y, is given by p(1, 1) = 0.5, p(1,2)= 0.1, p(2, 1) = 0.1, p(2, 2) = 0.3 Calculate the conditional probability mass function of X given that Y = 1.f(x)= k(3x+4), x = -1,0,1,2 Find expected value E(X) . Select one: O a. 0.5 O b. 1 O c. 1.182 с. O d. 1.5
- The joint probability mass function of X and Y is given by p(1, 1) = 0.05 p(2, 1) = 0.1 p(1,2) = 0.05 p(1, 3) = 0.05 p(2,2) = 0 p(2, 3) = 0.05 p(3, 1) = 0.05 p(3,2) = 0.1 p(3, 3) = 0.55 (a) Compute the conditional mass function of Y given X = 2: P(Y = 1|X = 2) = ☐ P(Y = 2X = 2) = P(Y = 3|X = 2) (b) Are X and Y independent? (enter YES or NO) (c) Compute the following probabilities: P(X + Y > 2) = P(XY = 2) = P(¥ > 1) = |If the average number of rodents in a cotton farm whose swabs are 20 dunums is 2 per dunum, calculate The probability that a given dunam contains more than 3 rodents. b, find the value of the constant C that makes the following function a probability mass function F(x) C 0.15 0.45Consider the probability density fx (x) = a. eb x! where X is random variable whose allowable values range from x = -o to + o. Find (a) the CDF (b) the relation between a and b (c) the probability that x lies between 1 and 2.
- A shop receives a shipment of 1000 lamps. The probability that any individual lamp is defective is 0.2%. Assume the defectiveness is independent of cach lamp. Let X be the number of defective lamps in the batch of 1000. What is the probability mass function of X? O P(X = k) = (00) 0.002* (1 – 0.002)1000 , k = 0,1, 2, ..., 1000 O P(X = k) = 0.002* (1 – 0.002)1000–&, k = 0, 1, 2, .….., 1000 O P(X = k) = (1000) 0.002* (1 – 0.002)1000 , k = 1, 2, ..., 1000 O P(X = k) = (00)0.002100- (1 – 0.002)*, k = 0, 1, 2, ..., 1000Please show all stepslet x,y be two random variable with joint probability density function -1 0.1 0.2 0.1 0.2 0.1 0.2 1- Find E( x/y-0)