Answer to Question #224641 in Algorithms for hay

Question

Q1. A random variable is defined as “ thenumber 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.

   Q(2)A random variable is defined as Construct the probability distribution function  

      of X and find the standard deviation of X.   

 

Q(3)It is known that only 60% of a defected computer can be   

   repaired. A sample of 15 Pc is selected randomly,   

   find the probability that;

 (i) None can be repaired  ​        

 (ii) 5 or less can be repaired ​     

(iii) At least 3 computers can be repaired.

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

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