0.10 0sx<1 0.15 1 χ<2 0.40 2 <3 0.70 3 x <4 1 x24 7. (10...

Question

Question

math Statistics-And-Probability

Answer 1

Answer #1

To calculate P(a<X<b)
where a<b. Recall, that if F is the CDF of X then F(x)=P(X≤x) for all values x. Now use this in given problem

P(a<X<b)=P(X<b)−P(X≤a)

P(0<X<4) = F(4) - F(0) = 0.70 - 0 = 0.70

Answer 2

Similar Homework Help Questions

3. (10 points) Let X be a continuous random variable with CDF for x < -1...

3. (10 points) Let X be a continuous random variable with CDF for x < -1 Fx(x) = { } (x3 +1) for -1<x<1 for x > 1 and let Y = X5 a. (4 points) Find the CDF of Y. b. (3 points) Find the PDF of Y. c. (3 points) Find E[Y]
2. For a discrete random variable X, with CDF F(X), it is possible to show that...

2. For a discrete random variable X, with CDF F(X), it is possible to show that P(a < X S b)-F(b) - F(a), for a 3 b. This is a useful fact for finding the probabil- ity that a random variable falls within a certain range. In particular, let X be a random variable with pmf p( 2 tor c-1,2 a. Find the CDF of X b. Find P(X X 5). c. Find P(X> 4). 3. Let X be a...
5. (Discrete and ontinuous random variables) (a) Consider a CDF of a random variable X, 10...

5. (Discrete and ontinuous random variables) (a) Consider a CDF of a random variable X, 10 x < 0; Fx(x) = { 0.5 0<x< 1; (1 x > 1. Is X a discrete random variable or continuous random variable? (b) Consider a CDF of a random variable Y, 1 < 0; Fy(y) = { ax + b 0 < x < 1; 11 x >1, for some constant a and b. If Y is a continuous random variable, then what...

(a) Below is the CDF for a discrete random variable, X if x 1 1/2 if...

(a) Below is the CDF for a discrete random variable, X if x 1 1/2 if 1 x< 2 if 2 x 3 7/8 if 3 x 4 F(x) = 3/4 2 1 if nx <n+1. Describe the probability 2n In general, note that for any positive integer n, F(x) distribution of X by finding P(X 1), P(X = 2), P(X positive integer n, and describe an experiment that would result in this random variable X. 3), and the general...
he cumulative distribution function (cdf), F(z), of a discrete ran- om variable X with pmf f(x)...

he cumulative distribution function (cdf), F(z), of a discrete ran- om variable X with pmf f(x) is defined by F(x) P(X < x). Example: Suppose the random variable X has the following probability distribution: 123 45 fx 0.3 0.15 0.05 0.2 0.3 Find the cdf for this random variable
1. Find Fx in terms of φ (t). Is X a continuous random variable ? 2. Compute p(X 0) 3. Compute E(...

1. Find Fx in terms of φ (t). Is X a continuous random variable ? 2. Compute p(X 0) 3. Compute E(X). Hint: use the CDF expectation formula, and integration by parts. You may assume that lim, t"o(-t) 0 for all n 2 0. 4. Find the CDF Fx (u) 5. Compute V(X). Hint: use Fxa, and follow the same hint of part (3) 1. Find Fx in terms of φ (t). Is X a continuous random variable ? 2....

0.25 x-1 0.15 x2 6. Let X be a discrete random variable with PMF: Px(x) 0.2...

0.25 x-1 0.15 x2 6. Let X be a discrete random variable with PMF: Px(x) 0.2 x-3 0.1 x 4 0.3 x-5 0 otherwise a. (10 points) Find E[X] b. (5 points) Find Var(X)
Additional Problem 3. If X is a continuous random variable having cdf F, then its median...

Additional Problem 3. If X is a continuous random variable having cdf F, then its median is defined as that value of m for which F(m) = 0.5. Find the median for random variables with the following density functions (a) f(r)-e*, x > 0 (c) f(x) 6r(1-x), 1. Additional Problem 6. Let X be a continuous random variable with pdf (a) Compute E(X), the mean of X (b) Compute Var(X), the variance of X. (c) Find an expression for Fx(r),...
Additional Problem A: The CDF of random variable X is given by: I< -3 -3 <...

Additional Problem A: The CDF of random variable X is given by: I< -3 -3 < z< -2 Fx(r) = -2 <I< 2 a) Find the possible range of values that the random variable can take. b) Find E(X) = 4x, the expec ted value. c) Find P(X > 1). d) Find P(X > 1|X > -2).

Consider the sample space S = {-3,-1, 0, 2, 4} and the events A = {-1,...

Consider the sample space S = {-3,-1, 0, 2, 4} and the events A = {-1, 0}, B = {0, 2}, and C = {-3, 0, 4} derived from the discrete random variable X. Let the probability of each outcome be as listed in the table below. Outcome (X) Probability −3 0.10 −1 0.20 0 0.30 2 c 4 0.25 Outcome (X) l Probability -3 0.10 -1 0.20 0 0.30 2 c 4 0.25 a) Find the value of the...