Please Help..(check answers)

#1
Can someone help me on these statistic questions. (FYI:i am not really good with probability..)
1.Family size can be represented by the random variable X. Determine the average family size...X- 2 3 4 5
P(x) .17 .47 .26 .10
a.2.94 b.3.00 c.3.29 d.3.49 e.3.86 i got c as my answer.

which of the follwoing is not true concerning discrete probability distribution?
a.the probability of any specific value is between 0 and 1.
b.the mean of the distribution is between the smallest and largest value in the distribution.
c.the sum of all probabilitites is 1.
d.the standard deviation of the distribution is between -1 and 1.
e.the distribution may be displayed using a probability histogram.
i narrowed this one down to either d or b.

3.The independent random varibables X and Y are defined by the follwoing probability distribution tables.
X 1 3 6 Y 2 3 5 7
P(x) .6 .3 .1 P(Y).1 .2 .3 .4

Determine the mean of X+Y. I got 7.2

If the standard deviation of Y is 1.81, determine the standard deviation of 3Y+5. (i dont get what to do on this one)
Possible answers to the question above. a).44 B)3.62 C)0 D)5.10 E)5.44

If the standard deviation of Y is 1.81 and the standard deviation of X is 1.58, determine teh standard deviatiion of X-Y. (Do you just subtract)???
possible answer:a.5.773 b.0.883 c.0.230 d.2.403 e.cannot be determined form the given information.

i am not looking just for answers to these question but would appreciate if someone could explain on what to do...
 

ssd

New Member
#3
1/ 2*0.17+3*0.47+4*0.26+5*0.1
2/ d,e
3/ As in 1/ find mean of X and of Y separately and add
4/ SD(3Y+5)=3*SD(Y)
5/ V(X-Y) = V(x)+V(Y)-2Cov(X,Y)
V(X)+ SD(X)*SD(X)
If X&Y are uncorrelated then Cov(X,Y)=0
Then V(X+Y)=V(X)+V(Y)
SD(X+Y)= Sqrt(V(X+Y)
If X&Y are not uncorrelated then SD(X+Y) cannot be determined from
SD(X) and SD(Y) only.