Question 347576: could you please help me with my probability assignment. I am having troubles answering the questions.
3. For the probability distribution table below:
x=1 Pr(X)=a ,x=2 Pr(X)=0.1 ,x=3 Pr(X)=2a ,x=4 Pr(X)=0.2 ,x=5 Pr(X)=3a ,x=6 Pr(X)=0.3 ,x=7 Pr(X)=2a.
a.) Determine the value of a so that the table represents a valid probability distribution
b.) Calculate the expected value of the distribution.
4. Consider a probability distribution defined by the rule;
P(x) =2x+1/35, for x=1, 2, 3, 4, 5.
a.) Confirm that this is a valid probability distribution.
b.) Calculate E(X).
c.) Calculate E(X^2).
d.) E(3X)
e.) Var(X)
f.) SD(X)
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! a) Hint: All of the probabilities should add up to one. So 
b) Expected value =  . So simply multiply each x value with its corresponding probability and then add up those products to get the expected value.
c) First square each x value. Then follow the same procedure done in part b)
d) This time, you're going to triple each x value. Then you're going to follow the same guidelines in part b)
e) First subtract each x value from the expected value (or mean) found in part b). Then square those differences. After that, multiply those results by each corresponding probability. Finally, add up all of the previous results to get the variance.
f) Take the square root of the answer found in part e) to get the standard deviation.
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