Question

Random Variables and Distributions MATH HELP PLZ!

Answer 1

For the first part: A frequency distribution is a valid probability distribution if all the probabilities add up to 1.

Answer 2

Hints:
1. probability distributions never go negative, zero sometimes.
2. The integral (or summation) of the distribution over its domain always equals 1.

Answer 3

Part 2:
Integrate or sum over given interval to get the probability of X\(\in\)given interval.

Answer 4

@DanJS

Answer 5

Q3:
E(X)=\(\sum x p(x)\) or \(\int x p(x) dx\) depending on whether distribution is discrete or continuous.

Answer 6

Q4.
P(succeeds one throw)=0.65=p
Use either the binomial coefficients or the multiplication rule to calculate the probability of succeeding 0,1 or 2 throws out of two free throws.
Remember that the probabilities must add up to one, because the domain is {0,1,2}.

Answer 7

Q5.
Assuming the figure shows the complete distribution, i.e. probability is 0 elsewhere, then P(X<27) is the ratio of the area below 27 over the total area.

Answer 8

Q6. similar to Q5.

Answer 9

Calculate Z=\(\dfrac{X-\mu}{\sigma}\)
where
\(\mu=mean\) and \(\sigma=standard~deviation\)
X=280, \(\mu=290\), and \(\sigma=10\)
Look up the normal probability distribution table (left tail) for the calculated Z for P(X<280)

Answer 10

Q8.
Similar to Q7.