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Probability course is not being taught in mathematics but its important in engineering, physics, computer science etc. Every science field. This is solved assignment for Probability. It includes: Probability, Destiny, Function, Statistical, Notations, Calculus, Integrate, Margin, Distribution
Typology: Exercises
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The current assignment will help out students for:
Understanding about the application of probability distributions. Establishing the link between discrete probability distribution and continuous probability distribution. Getting hands-on practice to find out the joint probability distribution.
Assignment No: 3 (Lessons 23-30)
Question 1: Marks: 5 +
The probability density function of a random variable is given
f(x) = 2(x-1) 1<x < 2 0 Elsewhere Calculate second moment about origin.
Sol
2 2
2 2
2 2 2 1 2 3 2 1 2 2 3 2 1 1 4 2 32
1 1 4 4 3 3
E x x f x dx
E x x x dx
E x x x dx
x x dx
x dx x dx
x x
b) Let x and y are two independent r.v.’s with joint probability density function.
Find the marginal probability density function g(x).
Sol
= 0, elsewhere.
We will use the continuity correction for finding the required probability. The interval at least 25 indicates 25; therefore it starts at 24.5 to infinity by continuity correction
X 1/ 2 Z
By using area table, we can easily find = 0.3643 + 0.5 = 0.