Bivariate normal distribution with parameters
Let the continuous random variables X and Y follow a bivariate normal distribution with parameters
μx=3, μy = 1, σ2x=16, σ2y=4 and ρ=1/2. Find the probability that X falls between 1 and 4 given that Y equals 2.
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Determine and equation of form y = asinwt which provides distance of the mass from its rest position as the function of time.
Let X follow a unifor distribution U(0,2) and let conditional distribution of Y given X = x be U(0,x2). Determine the conditional expectation of Y given X = x?
One thousand raffle tickets are sold for $2.00 each. One grand prize of $700 and two prizes of $100 each will be awarded. Tim buys one ticket. Determine the expected value.
Of the 25 animals at animal shelter, 15 are dogs. Two animals are selected at random. Determine exact odds that both are dogs?
Let the continuous random variables X and Y follow a bivariate normal distribution with parameters. μx=3, μy = 1, σ2x=16, σ2y=4 and ρ=1/2. Find the probability that X falls between 1 and 4 given that Y equals 2.
A new chairman wants the 5 labor unions to take a wage cute. Assume there is a .7 probability that a union will reject a wage cut and that the decisions are independent of each other. Determine the probability that
Draw the graph of function f(x)= 2 cos 3x over interval (0, 2π) and find points where function reaches its local maximum and local minimum within above interval.
Let X be the number of heads obtained in 5 tosses of a fair coin. Let -∞<t<∞ and define g(X)=e^tx. M(t)=E(e^tx)=Sg(x)f(x)=(x=5 above)Σ(x=0 below)= (5 choose x) ((1/2)^5)(e^tx)
On what day is there most daylight and least and how much daylight is there on the days? Determine the period of the function?
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