Let the joint density function of the random variables X and Y be fX, Y px, yq " # 2xex 2´y 0 ă x ă 1, y ą x 2 0 otherwise (a) Find the marginal density function of X. (b) Find the marginal density function of Y . (c) Compute the probability PpY ă 3X2 q.

Muscles, a membership-only gym is hoping to open a new branch in a small city in pennsylvania that currently has no fitness centers. according to their research approximately 12,600 residents live within driving distance of the gym. muscles sends out surveys to a sample of 300 randomly selected residents in this area (all of who respond) and finds that 40 residents say they would visit a gym if one was located in their area. based on the past survey research, muscles estimates that approximately 30% of these respondents would actually join the gym if they opened one in the area. based on this information and the results of the sample survey, about how many residents should muscles expect to join its new branch? a) 134 b) 504 c) 1,680 d) 3,780

State whether weight is a function of height for the six students and explain. a. yes, height is a function of weight because two students weigh 165 pounds but have different heights. b. no, height is not a function of weight because two students weigh 165 pounds but have different heights. c. yes, weight is a function of height because for each value of height there is one corresponding value of weight. d. no, weight is not a function of height because there is not enough data to determine a function.

Julian wrote the following numeric pattern on the board3,10,17,24,31,38.what numbers of julian's pattern are compound numbers.