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Box 1 contains 1000 bulbs of which 10% are defective. Box 2 contains 2000 bulbs of which 5%
are defective. Two bulbs are drawn (without replacement) from a randomly selected box. (i) Find the probability that both bulbs are defective, and
(ii) Assuming that both are defective, find the probability that they came from box 1.
A random vector (X1, X2) is a discrete random vector if its space D or range space is finite or countable. Suppose X1, X2 are positive integer valued and we need to find P(X1= x1, X2= x2), where x1, x2 are known positive integers, in terms of their known cumulative distribution function F.
Should the definition of random vector be associated with P: the probability set function?
Should the definition of random vector be associated with P: the probability set function?
1.3 The monthly salaries of the employees at Lyman Limited follow a normal distribution with an average salary of R 14 000 and a standard deviation of R 500.
a) What percentage of employees get paid between R 13 000 and R 15 500?
(i) C(X +Y,Z)= C(X,Z)+C(Y,Z), where X and Y are two random vectors of the same dimension and C(X,Z)=C(Z,X).
(ii) If m=n, V(X+Y) =V(X) + V(Y)+ 2C(X,Y).
Suppose (X,Y,Z)^T has exponential distribution with mean vector (1,2,3)^T . Find the correlation matrix of (X,Y,Z)^T .
Given that a person’s last chocolate purchase was kitkat, there is a 75% chance that his
next chocolate purchase will also be kitkat. 5% chance that his next chocolate purchase
will be park. If a person’s last chocolate purchase was park, there is an 70% chance that
his next chocolate purchase will be kitkat. 10% chance that his next chocolate purchase
will also be park. If a person’s last chocolate purchase was dairy milk, there is an 90%
chance that his next chocolate purchase will also be dairy milk, 5% of kitkat and 5% of
park.(a) You may buy daily milk today with a chance of 99%. What is the probability that after 3 purchase you will switch to kitkat?
(b) Does this statement proof long run property of markov chain
steady state probabilities?
Show that, if A>0, then
i) A is non singular and |A| >0
ii) A inverse > 0
The random variable represents the amount gain by a person who buys a 20peso ticket from a total of 1000 tickets for a raffle whose winner will obtain ₱5,000.
#340153 on Dec 2023