Question

Please solve the following problems step by step and write down the solving details as much as you can

Q5. The random variable N has PMF Sc(1/2)", п- 0, 1,2 1 0, PN(n) = { (1) otherwise (10%) (10%) (a) What is the value of the constant c? (b) What is P[N < 1]?

Answer 1

For to represent a probability mass function, required conditions are :

Pn(n)

i) for all values of n

Pn(n) > 0

ii)

Σ ΡΝ (n) =1

a) To find c such that

ΣΡΝ (n) =1 n=0

- ( + ( + ( = 1

= c[1+5+

T- 4 C*

(ans)

c=

So, The probability mass function of N is

px(n) = + (+)", n = 0,1,2

b) ​​​​​​​

P(N<1) = p (0) + pN(1) = من انا