The ratio of defected switches in the production of

these lines is 0.03 , 0.04, 0.01, 0.02 and 0.01 respectively, and

required the following:

a We draw a transistor of the total production of the factory,

what is the probability that this transistor is defected ?

b If we have found that the drawn transistor is not defected,

what is the probability that this drawn transistor from the

first line of factory ?

Q3 Answer the following questions about bivariate normal random variables. a. Suppose X and Y are dependent bivariate normal random variables. Then the correlation between X and Y: is positive. equals zero. is negative. may be positive or negative, but is nonzero. cannot be determined without additional information. Submit Answer Tries 0/10 b. The bivariate normal distribution has location parameters /x and My. O True. False. Submit Answer Tries 0/10 c. Consider the countour plot of bivariate normal random variables (X, Y) when ux = 8. ox = 3. My = 6, cy = 5, and p = -0.7. The contours look like: concentric circles around the point (8. 6). concentric ellipses having center (8. 6) and tilted along a line that has positive slope. one straight line with slope -0.7. two straight lines, one with slope -0.7 and one with slope 0.7. concentric ellipses having center (8, 6) and tilted along a line that has negative slope. Submit Answer Tries 0/10Consider bivariate continuous random variables, X and Y, with the following joint PDF. Are X and Y independent? fxr(x.v) = 4x - 2y for 0 x = 1, and O EVE x O . The answer cannot be determined from the given information. O D. No O C Yes2. Let bivariate continuous random variables ) and X, have the following joint probability density function. fx x, (x , x2 ) = 3x, , for OS x, Six, $1 (a) Find the marginal probability density functions of X, and X, (b) Find P X, S-, X2 S (c) Find P X, SIX, S NI- (d) Find the conditional probability density function of X, given X, = X2 .Answer all the following questions Consider the bivariate random vector 1. Expand the matrix form of the density function to get the usual bivariate normal density involving 01, 02, p and exponential terms in (21 - (1)2, (11 -(2) and (12 -(2)2. 2. Explain what happens in the following scenarios: (a) p=0 (b) p = 1 (c) p= -1