Search & Filtering
Define a filter in time series analysis. Find the effect of a linear filter on the time series
Xt=cosθt+isinθt
What role does ANOVA play in the design of experiments
What is the difference between a fixed effects model and a random effects model for the randomized block design
Suppose the joint p.d.f of the continuous random variable X and Y is given by
f(x,y)=λ2e(-λ(x+y)) zero otherwise x>0 y>0
i) Obtain the joint p.d.f of the new random variables V=X+Y and U=X/(X+Y)
ii)Find the marginal probability distribution functions of U and V
iii) Determine whether or not U and V are independent
The random variables X and Y have joint p.d.f given by
f(x,y)=k, 0<x<y<2 zero otherwise
i) Obtain the value of the constant k
ii)Find the conditional variance of Y given X=x
Established 95% and 99% confidence interval about the mean for a psychological test that is given to thirty two persons and has a mean of 53 and a standard deviation of 7.5 assuming that the population standard deviation is not known.
The random variables X and Y are bivariate normal distributions with parameters µx=5,
µy=10,σ2x=16,σ2y=9 and ρ=0.3. what is the conditional probability distribution of Y given X=x.
Let X and Y be discrete random variables with joint probability distributions given by
f(x,y)=1/4, x=1,2 and y==1,2 zero otherwise.
i)Find the joint moment generating function of X and Y
ii)Using the joint m.g.f obtain in (i) find the covariance between X and Y
iii)Determine whether or not X and Y are independent
The joint probability distribution of X and Y is given by
f(x,y)=x+y, 0<x<1 and 0<y<1 zero otherwise.
Determine the joint distribution function of X and Y i.e F(x,y). Hence or otherwise calculate p(0<x<1/2,1/2<y<1)
if X and Y are random variables such that Var(X)<∞ and Var(Y)<∞,show that
Var(aX+bY)=a2Var(X)+b2Var(Y)+2ab cov(X,Y). Where a and b are real constants.
#340153 on Dec 2023