Question

Construct the discrete probability distribution for the random variable described. Express the probabilities as simplified fractions. The number of heads in 4 tosses of a coin.

Answer 1

Answer:

Discrete probability distribution

X           0      1        2       3     4

P(X=x)  1/16  4/16  6/16  4/16  1/16

Step-by-step explanation:

Discrete Random variable:-

A random variable X which can take only a finite number of discrete values

In an interval domain is called a discrete random variable. In other words

a real valued function defined on a discrete sample space is called a

Discrete Random variable.

For example : X(s) = { s: s = 0, 1, 2} The random variable X is a discrete Random variable.

Given the number of heads in 4 tosses of a coin

The total number of possible events is n(S) = 2^4 = 16

Discrete distribution:-

The random variable X is a discrete Random variable.

X(x) = { x: x = 0, 1, 2,3,4}

Here x=0 means → no heads that is the possible outcomes are only one

n(E) = {T,T,T,T} = 1

P(X=0) = $=\frac{1}{16}$

Here x=1 means → one head and three tails that is the possible outcomes are '4'

n(E) ={( HTTT),(THTT),(TTHT),(TTTH)

$P(x=1) = \frac{4}{16}$

Here x=2means → TWO head and TWO tails that is the possible outcomes are '6'

n(E) = {( HHTT),(THHT),(TTHH),(HTTH),(THTH),(HTHT)

n(E) = 6

$P(x=2) = \frac{no of possible events}{1total no of possible events}$

$P(x=2) = \frac{6}{16}$

Here x=3means → three head and one tails that is the possible outcomes are '4'

n(E) = { HHHT,HTHH,HHTH,THHH} =3

$P(x=3) = \frac{4}{16}$

Here x=4 means → FOUR heads that is the possible outcomes are only one

n(E) = {HHHH} = 1

$P(x=4) = \frac{1}{16}$

Final answer:-

Discrete probability distribution

X           0      1        2       3     4

P(X=x)  1/16  4/16  6/16  4/16  1/16