(from an actuarial exam) the random variables x and y have joint probability mass function p(x, y) for x = 0, 1 and y = 0, 1, 2. suppose that 3p(1, 1) = p(1, 2) and p(1, 1) maximizes the variance of xy . calculate the probability that x or y is zero.

0.4696

Step-by-step explanation:

Step 1: we say,

p(0,1) + p(0,2) + p(1,1) + p(1,0) + 3p(1,2) + p(0,0) = 1

P(Y=0) + p(X=0) - p(X=0, Y=0) + 4p(1,1) = 1.

Step2: let p(1,1)= w.

Therefore, 3w= p(1,2)

E(XY)= 2p(1,2) + p(1,1)

= 7w.

E[(XY)^2] = 4p(1,2) + p(1,1)

=13w.

variance(XY) = E[(XY)^2] - [E( XY)]^2

= -49w+ 13w

therefore, 0,1 are elements of w.

Step 3: calculate the derivative

13= 2x × 49

X = 13÷98

X= 0.1326

X=0, Y=0 = 1

= 1 - [0.1326 × (-4)]

= 0.4696.

7

step-by-step explanation:

i'm assuming you need to figure out how many campers go into each tent.

i got the answer by:

24+4=28

28/4=7  

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.