the random variable ,b, has a bernoulli distribution having pie = 0.17. what is the smallest value that b could have
A random variable B~Bernoulli Distribution can have only two values 0 or 1.
The only parameter of Bernoulli Distribution is p(pie) lies between 0 and 1.
Therefore the possible smallest value that B could have is 0.
the random variable ,b, has a bernoulli distribution having pie = 0.17. what is the smallest...
Question 3: A random variable X has a Bernoulli distribution with parameter θ є (0,1) if X {0,1} and P(X-1)-θ. Suppose that we have nd random variables y, x, following a Bernoulli(0) distribution and observed values y1,... . Jn a) Show that EIX) θ and Var[X] θ(1-0). b) Let θ = ỹ = (yit . .-+ yn)/n. Show that θ is unbiased for θ and compute its variance. c) Let θ-(yit . . . +yn + 1)/(n + 2) (this...
7. Let X1,....Xn random sample from a Bernoulli distribution with parameter p. A random variable X with Bernoulli distribution has a probability mass function (pmf) of with E(X) = p and Var(X) = p(1-p). (a) Find the method of moments (MOM) estimator of p. (b) Find a sufficient statistic for p. (Hint: Be careful when you write the joint pmf. Don't forget to sum the whole power of each term, that is, for the second term you will have (1...
Recall that a Bernoulli random variable with parameter p is a random variable that takes the value 1 with probability p, and the value 0 with probability 1 - p. Let X be a Bernoulli random variable with parameter 0.7. Compute the expectation values of X, denoted by E[X*1, for the following three values of k: k = 1,4, and 3203. E [X] = E [X4 E [X3203
A random variable X following the Bernoulli distribution with shape param- eter p has probability density function (pdf) given by f(x) = p x (1 − p) 1−x x = 0, 1 0 otherwise Show that a) P1 x=0 f(x) = 1 [5 Marks] b) E[X]=p [5 Marks] c) Var[X]=p(1-p) [5 Marks] d) the MGF of X is given by (1 − p) + pet
The probability distribution for the random variable x follows. 20 24 32 35 f(x) 0.25 0.17 0.27 0.31 a. Is this a valid probability distribution? Select b. What is the probability that x 32 (to 2 decimals)? c. What is the probability that x is less than or equal to 24 (to 2 decimals)? d. What is the probability that x is greater than 32 (to 2 decimals)?
The probability distribution for the random variable X is given below. X 0 P(x) 0.05 0.17 0.26 2 3 4 0.24 0.28 What is the standard deviation to the nearest hundredth) for the random variable? O A 1.17 OB. 12 O C. 1.3 OD. 124 O E. None of the above Click to select your answer Type here to search o i E
The Bernoulli random variable takes values 0 and 1, and has probability function f(x) = px (1 − p)1−x(a) By calculating f(0) and f(1), give a practical example of a Bernoulli experiment, and a Bernoulli random variable. (b) Calculate the mean and variance of the Bernoulli random variable.
A continuous random variable X has a normal distribution with mean 169. The probability that X takes a value greater than 180 is 0.17. Use this information and the symmetry of the density function to find the probability that X takes a value less than 158.
You know that a random variable has a normal distribution with standard deviation of 16. After 10 draws, the average is -12. What is the standard error of the average estimate? If the true mean were -11, what is the probability that we could observe a value between -10.5 and -11.5? You know that a random variable has a normal distribution with standard deviation of 25. After 10 draws, the average is -10. a. What is the standard error of...
. The two questions that follow concern the following variant of the Bernoulli pro- cess: Fix k 2 1. At each (integer) time n 2 1 the process takes the value Xn, where Xn are i.i.d. random variables each with the uniform distribution on 12,,. (4) (a) What is the PMF for the random variable N defined as the smallest N 2 2 so that XN X1 (b) Is N a stopping time? (c) What is the probability that XN+1...