4.1-1. For each of the following functions, determine the constant
c
so that
f(x,y)
satisfies the conditions of being a joint pmf for two discrete random variables
x
and
Y
: (a)
f(x,y)=c(x+2y),x=1,2,y=1,2,3
. (b)
f(x,y)=c(x+y),x=1,2,3,y=1,dots,x
. (c)
f(x,y)=c,x
and
y
are integers such that
6<=x+y<=8,0<=y<=5
. (d)
f(x,y)=c((1)/(4))^(x)((1)/(3))^(y),x=1,2,dots,y=1,2,dots
.

Question

4.1-1. For each of the following functions, determine the constant

c

so that

f(x,y)

satisfies the conditions of being a joint pmf for two discrete random variables

x

and

Y

: (a)

f(x,y)=c(x+2y),x=1,2,y=1,2,3

. (b)

f(x,y)=c(x+y),x=1,2,3,y=1,dots,x

. (c)

f(x,y)=c,x

and

y

are integers such that

6<=x+y<=8,0<=y<=5

. (d)

f(x,y)=c((1)/(4))^(x)((1)/(3))^(y),x=1,2,dots,y=1,2,dots

.

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