Problem 1. Sum of two random variables
Two independent uniform random variables: X and Y. The pdf of X is 1 when 0≤ x ≤1 and the pdf of Y is 1 when -0.5 ≤ y ≤ 0.5. Find the pdf of X+Y.
Problem 2. rv correlation
x1, x2, x3 are zero mean Gaussian random variables with STD=4. Let x1 and x2 be independent and x3= a*x1+b*x2. Find the constants "a" and "b" such that the correlation between x1 and x3 is 0.3. What is the correlation between x3 and x2?
Problem 3. Uniform Random Variable
A random variable x is uniformly distributed in the interval [5 10].
What is the pdf of x?
What is the CDF of x?
What is the pdf of y=3*x+10?
Problem5 Unifrom
1. Let x be a random variable uniformly distributed between 0 and 1. Generate 1000 x’s. If n(k) represents the number of x’s such that k*0.1>x³ (k-1)*0.1, plot n(k) with k=1,2,3,…,10.(hint: use rand and hist commands in matlab)
Attachment:- assignment_file.docx