Question

1)list all the possible outcomes using the tree diagram
2) determine the sample space.
3) determine the possible values of the random variables
4)assign probability values p(x) to each of the random variable
5) construct a probability histrogram to describe the p(x).
please help po​

Answer 1

1 . Probability Tree Diagrams

The probability of "Head, Head" is 0.5×0.5 = 0.25.

All probabilities add to 1.0 (which is always a good check)

The probability of getting at least one Head from two tosses is 0.25+0.25+0.25 = 0.75.

2. The size of thesample space is the total number of possible outcomes. For example, when you roll 1 die, the sample space is 1, 2, 3, 4, 5, or 6. So the size of thesample space is 6. Then you need to determine the size of the eventspace.

3. Step 1: List all simple events in sample space. Step 2: Findprobability for each simple event. Step 3: List possible values forrandom variable X and identify thevalue for each simple event. Step 4:Find all simple events for which X = k, for each possible value k.

4. For a simulation, I want to construct the probability distribution of a random variable XkXk that takes only finite number of values x1,⋯,xNx1,⋯,xN. I have to assign values to each probability: Pr(X=x1),⋯,Pr(X=xN)Pr(X=x1),⋯,Pr(X=xN), and of course they should sum to one: ∑Ni=1Pr(X=xi)∑i=1NPr(X=xi). I have two ways in my mind:

1) I generate NN values using a continuous uniform random number generator, and then divide each by the total.

2) I generate N−1N−1 values using a continuous uniform(0,1) random number generator, sort them out and treat these numbers as cut points for the probabilities.

What can I say about these two ways? Are they equivalent in the sense that the distributions of the generated probabilities are the same? If different, is there any reason to choose one over the other?

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5 . i dont know sorry