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Find the approximate value of constant c for a standard normal random variable such that:
a) For c>0, P(0<Z<c) = 0.48382
b) For c>0, P(-c<Z<c) = 0.95000
Does anyone know how to approach this?
If a set of observations is distributed as N(u, std. dev.^2), what is the percentage of the observations will differ from the mean by:
a) less than 1 standard deviation?
b) less than 2 standard deviation?
C) less than 3 standard deviation?
How can I prove this?
If a random variable X is defined such that E[(X-1)^2]=10 and E[(X-2)^2]=6, find the mean and variance of X.
Does anyone know how to approach this question??
Here is what I got so far:
E[(X-1)^2]=10 : E(X^2) - 2E(X) + 1= 10
E[(X-2)^2]=6: E(X^2) - 4E(X) + 4= 6
What should I do next to get the mean and variance?
Given random variable X with standard deviation x, and a random variable Y=a + bX, where a,b are constants, show that if b<0, the correlation coefficient = -1, and if b>0, correlation coefficient is 1.
Does anyone know how to prove this?
The government is building 2 bridges. 3 firms are submitting bids for the work: Firm #1, Firm #2, Firm #3. The government will not give both contracts to the same firm. Let random variable X=1 if Firm #1 gets a contract, and X=0 if Firm #1 does not get a contract. Similarly, let random variable Y=1 if Firm #2 gets a contract, and Y=0 if Firm #1 does not get a cotract. Note that X and Y are jointly distributed.
1) List all possible outcomes. Determine the values X and Y for each possible outcome.
Does anyone have an idea how to approach this?
For b, you can use binomial distribution!!
Suppose a coin is tossed until a head appears. Let p be the probability of a head on any given toss. Define random variable X to be the number of tosses required to obtain a head.
a) State the set of values that X can take on. Is this finite or countably infinite set?
b) What is the PMF (probability mass function) of X? If p = 1/4, what is the probability that X=10?
Can any one help on this question??
An insurance company writes a policy such that an amount of money A must be paid if some event E occurs within a year. If the company has estimated that event E will occur within a year with probability p, how much should the company charge its customer so that its expected profit will be 10% fo A?
Does anyone know how to approach this question?
The C.D.F. (cumulative density function) of the random variable X is given by,
F(x)= [0, x<0
x/2, 0<=x<1
2/3, 1<=x<2
11/12, 2<=x<3
1, 3<=x]
a) Find P(X>1/2)
b) Find P(2<X<=4)
c) Find P(X=1)
Does anyone know how to approach this?
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