What is the probability of exactly 4 successes

Assignment Help Advanced Statistics

Reference no: EM133651320

Question 1: If x is a R. V which has the probability function find MGF, mean & Variance. P(X) = 1/k^x, x = 1,2,3..

Question 2: Find MGF and r^th moment of the R.Variable X, whose pdf

f ( x ) = ke^-x, x > 0

Question 3: Find the MGF of a random variable x having the PDF

f(x) = 1/3 , x > -1 < x < 2 and find mean & Variance.

f(x) = 0 , otherwise

Question 4: Find the MGF of R. variable X whose probability Density Function ( PDF ) is given by f (x) = λe^-λ(x-a), x ≥ a and hence find its mean and Variance

Question 5: Find the MGF of R. variable X whose PDF is f(x) = x/4 e^-x/2, x > 0. Also find the first 4 moments about the origin.

Question 6: In each of 4 races, the Democrats have a 60% chance of winning.

Assuming that the races are independent of each other, what is the probability that:

a. The Democrats will win 0 races, 1 race, 2 races, 3 races, or all 4 races?
b. The Democrats will win in at least 1 race
c. The Democrats will win a majority of the races

Question 7: If X is binomially distributed with 6 trials and a probability of success equal to 1/4 at each attempt, what is the probability of
a) Exactly 4 successes?
b) at least one success?

Question 8: When an unbiased coin is tossed eight times what is the probability of obtaining :
a) Less than 4 heads b) More than five heads?

Question 9: A biased die is thrown thirty times and the number of sixes seen is eight. If the die is thrown further twelve times find:
a) The probability that a six will occur exactly twice.
b) The excepted number of sixes
c) The variance of the number of sixes

Question 10: A random variable X is binomially distributed with mean 6 and variance 4.2. Find P(X< 3).

Reference no: EM133651320

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