Consider the experiment of tossing a coin twice.

a. List the experimental outcomes. (Let H represent a coin landing on heads and T represent a coin landing on tails.)
b. Let denote the number of heads occurring on two coin tosses. Show what value the random variable would assume for each of the experimental outcomes.
c. Define a random variable that represents the number of heads occurring on the two tosses.
d. Is this random variable discrete or continuous?

Answer:

Kindly check explanation

Step-by-step explanation:

Experiment of tossing a coin twice :

A.) Experimental outcome:

Head = H ; Tail = T ;

Head and Head = HH

Tail and Tail = TT

Head and Tail = HT

Tail and Head = TH

Number of head(s) on toss = z

C)

Experimental outcome ___number of heads(z)

HH _____________________2

TT _____________________ 0

TH _____________________ 1

HT _____________________ 1

D) the random variables defined are discrete because they are only take up integer values within a specified range

The following conclusions of the random variable will be

a. Total outcome = 4 {HH, HT, TH, TT}

b. The experimental outcomes = 2 {TH, HH}

c. The experimental outcomes = 1 {HH}

d. Random variable is discrete.

Random variables are rules relating the sample space's elements to real numbers.

Those random variables, which take only distinct values, are called discrete random variables.

Those random variables, which take any value from a given continuous interval of real numbers are called continuous variables.

The experiment of tossing a coin twice.

The total number of outcomes will be

Total outcome = 4 {HH, HT, TH, TT}

a. List the experimental outcomes.

Total outcome = 4 {HH, HT, TH, TT}

b. The number of heads occurring on two coin tosses.

The experimental outcomes = 2 {TH, HH}

c. A random variable that represents the number of heads occurring on the two tosses.

The experimental outcomes = 1 {HH}

d. Random variable is discrete.

More about the random variable link is given below.

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