p-p-131

Q #1.

Determine the value of C so that the following functions represent probability distinguish of the random variables x & y? a)

f(f(x, y) =Cxy for x=1, 2, 3 y=1, 2, 3

y\x | 1 | 2 | 3 | h(y) ______|____________|___________|____________|__________ 1 | 1C | 2C | 3C | 6C 2 | 2C | 4C | 6C | 12C 3 | 3C | 6C | 9C | 18C ______|___________ |___________ |___________ |___________ g(x) | 6C | 12C | 36C | 36C 36C=1 C=1/36 C=xy/36 b)

f(x, y) =c|x-y| for x=-2, 0, 2 y=-2, 3 y\x | -2 | 0 | 2 | h(y) ______|____________|___________|____________|__________ -2 | 0 | 2C | 4C | 6C | | | | 3 | 5C | 3C | C | 9C ______|___________ |___________ |___________ |___________ | | | | g(x) | 5C | 5C | 5C | 15C | | | |

15C=1 C=1/15 Q #2. If the first probability dist. Of x & y is given by F(x, y) =x+y/30 for x=0, 1, 2, 3 y=0, 1, 2 y\x | 0 | 1 | 2 | 3 | h(y) ______|____________|___________|____________|___________ | 0 | 0 | 1/30 | 1/2 | 1/10 | 1 | 1/30 | 1/15 | 1/10 | 4/30 | 2 | 1/15 | 1/10 | 4/30 | 1/6 | ______|___________ |___________ |___________ |___________ |

a)

P(x2; yy) f(1,0)+f(2,0)+f(3,0)+f(2,1)+f(3,1)+f(3,2) =1/30+1/15+1/10+1/10+4/30+1/6 =3/5

d)

P(x+y=4) f(3,1)+f(2,2)=4/30+4/30 =4/5

Q No.3.

a)

A sack of fruit containing 3 oranges,apples and bananas.A random smple of 4 pieces fruit is selected. If x is the No. of oranges & y is the No. of apples in the sample find: The joint probability dist. Of x & y y\x | 0 | 1 | 2 | 3 ______|____________|___________|____________|__________ 0 | 0 | 3/70 | 9/70 | 3/70 1 | 2/70 | 18/70 | 18/70 | 2/70 2 | 3/70 | 9/70 | 3/70 | 0 ______|___________ |___________ |___________ |___________ | | | |

b)

{(x,y)|x+yIt is dependent

Q No 13.

Determine whether the two random variable of EX 11 are dependent or independent f(x,y) = g(x) h(y) f(2,1) = g(2)h(1) 0.10 = (.40)(.25) 0.10 = 0.10 => It is independent