For a discrete random variable X, it is known that Pr[X = 1] = 0.15, Pr[X...

For a discrete random variable X, it is known that Pr[X = 1] = 0.15, Pr[X = 3] = 0.3, Pr [X = 5] = 0.35, and Pr[X = 7] = 0.2. Find Pr[X < 5].

Expert Solution

P(X < 5) = P(X = 1) + P(X = 3) = 0.15 + 0.3 = 0.45 (ans)

orchestra answered 2 years ago

Let W be a discrete random variable and Pr(W = k) = 1/6, k = 1,...

Let W be a discrete random variable and Pr(W = k) = 1/6, k = 1, 2 ,....., 6. Define X = { W, if W <= 3; 1, if W >= 4; } and Y = { 3, if W <= 3; 7 -W, if W >= 4; } (a) Find the joint probability mass function of (X, Y ) and compute Pr(X +Y = 4). (b) Find the correlation Cor(X, Y ). Are X and Y independent? Explain.

1. The probability mass function of a discrete random variable X is defined as p(x) =...

1. The probability mass function of a discrete random variable X is defined as p(x) = ax for x = 1, 2, 4, 8 (p(x) =0 for all other values) then the value of a is? 2. Let X be a discrete random variable with Var(X) =6.0 and E(X2) = 17.00. Then: E(X) = ? 3. If X is a binomial random variable with parameters n and p, i.e. X ~ b(x; n, p), then the expected value of X...

LetXbe a discrete random variable with the following PMF: P(X=x) = 0.3 for x = 1,...

LetXbe a discrete random variable with the following PMF: P(X=x) = 0.3 for x = 1, a for x = 2, 0.5 for x= 3, 0 otherwise (a) Find the value of a. (b) Find Fx(x), the CDF of X. (c) What is the value of Fx(2)? (d) Find E[X]. (e) FindE[X^2]. (f) Find V ar(X) ---------------------- A certain area of the eastern United States is, on average,hit by 2 hurricanes a year. Find the probability that the area will...

1. (Memoryless property) [10] Consider a discrete random variable X ∈ N (X ∈ N is...

1. (Memoryless property) [10] Consider a discrete random variable X ∈ N (X ∈ N is a convention to represent that the range of X is N). It is memoryless if Pr{X > n + m|X > m} = Pr{X > n}, ∀m,n ∈{0,1,...}. a) Let X ∼ G(p), 0 < p ≤ 1. Show that X is memoryless. [2] b) Show that if a discrete positive integer-valued random variable X is memoryless, it must be a geometric random variable,...

The probability distribution of a discrete random variable x is shown below. X 0 &

The probability distribution of a discrete random variable x is shown below. X 0 1 2 3 P(X) 0.25 0.40 0.20 0.15 What is the standard deviation of x? a. 0.9875 b. 3.0000 c. 0.5623 d. 0.9937 e. 0.6000 Each of the following are characteristics of the sampling distribution of the mean except: a. The standard deviation of the sampling distribution of the mean is referred to as the standard error. b. If the original population is not normally distributed, the sampling distribution of the mean will also...

1. A coin is tossed 3 times. Let x be the random discrete variable representing the...

1. A coin is tossed 3 times. Let x be the random discrete variable representing the number of times tails comes up. a) Create a sample space for the event; b) Create a probability distribution table for the discrete variable x; c) Calculate the expected value for x. 2. For the data below, representing a sample of times (in minutes) students spend solving a certain Statistics problem, find P35, range, Q2 and IQR. 3.0, 3.2, 4.6, 5.2 3.2, 3.5...

The discrete random variable X is the number of passengers waiting at a bus stop. The...

The discrete random variable X is the number of passengers waiting at a bus stop. The table below shows the probability distribution for X. What is the expected value E(X) for this distribution? X 0 1 2 3 Total P(X) .20 .40 .30 .10 1.00 Answer the following questions using the given probability distribution. Expected value E(X) of the number of passengers waiting at the bus stop. Probability that there is at least 1 passenger at the bus stop. Probability...

The demand for a certain weekly magazine at a newsstand is a discrete random variable, X....

The demand for a certain weekly magazine at a newsstand is a discrete random variable, X. The demand never exceeds 6 magazines per week. The distribution of X is symmetric about the value of 3. 1. The table below is intended to present the distribution of variable X. Complete the table. x 0 1 2 3 4 5 6 P(X = x) 0.05 0.10 0.20 x 0 1 2 3 4 5 P(X=x) 0.05 0.10 0.20 2. The magazines cost...

give an example of a discrete random variable X whose values are integers and such that...

give an example of a discrete random variable X whose values are integers and such that E(X) = infinite. Prove that E(X) = infinite for your example. (hints: if you will be paid 2^k dollars for the kth head when you flip a fair coin., the expected value is infinite...) Or give other easy examples.

A discrete random variable named X has the following pmf (probability mass function): X P(x) 1...

A discrete random variable named X has the following pmf (probability mass function): X P(x) 1 0.6 3 0.2 7 0.1 11 0.1 17a) Find P(X>6) 17b) What is the probability two independent observations of X will both equal 1? 17c) Find the population mean also known as E(X)= the expected value of 17d) Find the population variance of X with both the “regular” formula and “convenient” formula Make a table and show your work. You should get the same...

Question