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Tamilnadu Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3

Question 1.
The probability density function of X is given by Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 111 Find the value of k.
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 1

Question 2.
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 2
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 3
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 4

Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3

Question 3.
Suppose the amount of milk sold daily at a milk booth is distributed with a minimum of 200 litres and a maximum of 600 litres with probability density function
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 16
Find (i) the value of k
(ii) the distribution function
(iii) the probability that daily sales will fall between 300 litres and 500 litres?
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 7
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 8

Question 4.
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 9
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 10
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 11
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 12

Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3

Question 5.
If X is a random variable with probability density function f(x) given by,
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 13
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 14
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 5

Question 6.
If X is the random variable with probability density function F(x) given by,
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 17 then find (i) the distribution function f(x)
(ii) P(0.3 ≤ X ≤ 0.6)
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 18

Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 Additional Problems

Question 1.
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 19
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 20

Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3

Question 2.
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 21
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 22
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 23
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 24

Question 3.
The probability density function of a random variable x is Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 25 Find
(i) k;
(ii) P(X > 10)
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 255
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 26

Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3

Question 4.
A continuous random variable x has the p.d.f. defined by Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 27 find the value of C if a > 0.
Solution:
Samacheer Kalvi 12th Maths Solutions Chapter 11 Probability Distributions Ex 11.3 277

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