Let the random variable Y have a geometric distribution with a mean of 3. The probability that P(Y24) is (a) 0.8683 (b) 0.0659 (c) 0.1976 (d) 0.3265

Assume, North Origano, is a country with highest domestic violence cases (approximately5 cases per 1000 families). Working with counselors, a researcher developed thefollowing probability distribution for x= the number of new clients for counseling for 2021. x f(x) 10 0.05 20 0.10 30 0.10 40 0.20 50 0.35 60 0.20 i. compute the expexted value and variance of X.

Consider the table below gives the probabilities of the distribution of random variable X. Value of X (x) P(X=x) (f(x)) 0 1 2 345 00 6 7 8 0.14 b C 0.10 0.13 0.13 d 0.02 0.01 In reference to the table, suppose that b = f(1) =0.15 and c = f(2)= 0.14. What is the probability P(2 ≤ X<7) equal to ?

In the probability distribution to the right, the random variable X represents the number of marriages an individual aged 15 years or older has been involved in. Compute and interpret the mean of the random variable X. Hx = marriages (Type an integer or a decimal. Do not round.) X 0 1 2 3 4 5 P(x) 0.264 0.567 0.136 0.029 0.003 0.001

Q7. A random variable X with a mean of 2.5 follows an exponential distribution. Find the following probabilities: (a) P(X > 2.5), (b) P(X xo) = 0.05.

Suppose the probability distribution of x, the number of defective tires on a randomly selected car checked at a certain inspection station, is given in the following table. 1 3 4 P(x) 0.60 0.14 0.05 0.03 0.18 (a) Calculate the mean value of x. (b) What is the probability that x exceeds its mean value?

Suppose the probability distribution of x, the number of defective tires on a randomly selected car checked at a certain inspection station, is given in the following table. 이 p(x) 0.60 0.14 0.05 0.03 0.18 X 0 1 (a) Calculate the mean value of x. 2 3 4 (b) What is the probability that x exceeds its mean value?

Let X be a binomial random variable with n = 400 trials and probability of success p = 0.1. Then the probability distribution of X can be approximated by Select one: a. another binomial distribution with n = 800, p = 0.2 %3D b. a Poisson distribution with mean 40. C. an exponential distribution with mean 40. d. a Hypergeometric distribution with N = 8000, n = 400, M = 40. %3D е. a normal distribution with men 40 and variance 36.

3. Find a z value such that the probability of obtaining a larger z value is only 0.15.

Suppose a random variable X is best described by a uniform probability distribution with range 0 to 6. Find the value of a that makes the following probability statements true. P( X > a ) = 0.13 P( 2.61 <= X <= a ) =0.03