Discrete random variable defined on a finite sample space

Assignment Help Mathematics

Reference no: EM13118455

Discrete Random Variable Defined on a Finite Sample Space
1. a) Prove that if X is a discrete random variable defined on a finite sample space, S, then we have E(X) = SUM X(a) P({a}).

b) Use part(a) to prove that if X and Y are discrete random variable defined on the same finite sample space S, then we have E(X + Y) = E(X) + E(Y).

2. Use the result of problem 1 above to show that the average number of heads when a fair coin is flipped n times is equal to n/2. Hint: Let H_i be the number of heads on the ith flip. {Note: compare this to the "brute-force" computation to get an interesting combinatorial identity!]

Reference no: EM13118455

Questions Cloud

What is the total sample size : What is the total sample size (in grams) for a sample of disulfur octoxide which contains 3.52 g of oxygen.

Determine probability theory : The answer to Probability theory It is found that when a particular 4-sided die is rolled a 1 occurs 22.8% of the time, a 2 occurs 25.3% of the time, a 3 occurs 20.8% of the time, and a 4 occurs 31.1% of the time.

Determine if tires were exceeding guarantee : Determine if the tires were exceeding the guarantee. At the .05 significant level, it was concluded that the tires are exceeding the manufacturer's guarantee.

How much energy in kilojoules is required : How much energy in kilojoules is required to convert 260 mL of water at its boiling point from liquid to vapor.

Discrete random variable defined on a finite sample space : Discrete Random Variable Defined on a Finite Sample Space. a) Prove that if X is a discrete random variable defined on a finite sample space, S, then we have E(X) = SUM X(a) P({a}).

Exponential and logarithmic functions : Convert the following equations into logarithmic form: How much interest will you accumulate if interest is compounded annually over the next five years?

Probability to obtain exactly two successes-bernoulli trials : You conduct 8 Bernoulli trials for which the probability of success is 0.85. What is the probability that you will obtain exactly two successes?

Determining inverse function and logarithm : Explain what an inverse function is and how you can determine when an inverse function will exist. What procedure is available to determine if two functions are inverses of each other? Explain its use and give an example.

Compute the probability an applicant''s gpa will be below : Probability distribution. The high school GPA of applicants for admission to a college program are recorded and relative frequencies are calculated for the categories.

User Account

All Pages