Question

Q1. A random variable is defined as “ the number of heads when
a coin tossed”,
(a)twice

(b)three times

(c)four times

(d)five times

Find the PDF of each of them and their respective mean and variance.

Answer 1

When fair coin is tossed,

The probability to get head = o.5

Probability to get tail =0.5

number of tossed count n = 2, 3, 4, 5

mean = np $=2\times 0.5 = 1$

n= 3

$3\times 0.5 = 1.5$

n= 4

$4\times 0.5 = 2.0$

n=5

$5\times 0.5 = 2.5$

variance $=n\times p\times (1-p)$

n=2

$=2\times 0.5 \times 0.5 = 0.5$

n=3

$=3\times 0.5 \times 0.5 = 0.75$

n=4

$=4\times 0.5\times 0.5 = 2.0$

n=5

$=5\times 0.5\times 0.5 = 1.25$