Probability mass function from given cumulative distribution function is given by,
x | 0 | 1 | 2 | 3 |
P(x) | 1/8 | (1/2)-(1/8)=3/8 | (7/8)-(1/2)=3/8 | 1-(7/8)=1/8 |
Option A) is correct.
X is a discrete random variable with cumulative distribution function F(x) as shown in the table...
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
2. Let X be a discrete random variable with the following cumulative distribution function 0 0.2 0.5 ェ<2, 2-1<5.7, 5.7-1 6.5, 6.5 <エ<8.5, F(z)= 18.5 エ a) Find the probability mass function of X b) Find the probabilities P(x>5), P(4<X 6x> 5) c) If E(X) = 5.76, find c.
(15 points) Let X be a continuous random variable with cumulative distribution function F(x) = 0, r <α Inr, a< x <b 1, b< (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
Show steps, thanks! 2.5.9. The random variable X has a cumulative distribution function 0, forx<0 F(x) for x > 0. for x > , 1+x2" · Find the probability density function of X.
Exercise 3.37. Suppose random variable X has a cumulative distribution function F(x) = 1+r) 720 x < 0. (a) Find the probability density function of X. (b) Calculate P{2 < X <3}. (c) Calculate E[(1 + x){e-2X].
12. (15 points) Let X be a continuous random variable with cumulative distribution function **- F() = 0, <a Inx, a < x <b 1, b<a (a) Find the values of a and b so that F(x) is the distribution function of a continuous random variable. (b) Find P(X > 2). (c) Find the probability density function f(x) for X. (d) Find E(X)
2). Consider a discrete random variable X whose cumulative distribution function (CDF) is given by 0 if x < 0 0.2 if 0 < x < 1 Ex(x) = {0.5 if 1 < x < 2 0.9 if 2 < x <3 11 if x > 3 a)Give the probability mass function of X, explicitly. b) Compute P(2 < X < 3). c) Compute P(x > 2). d) Compute P(X21|XS 2).
Suppose the cumulative distribution function of the random variable X is 0, x-0.8 F(x)-0.25x + 0.2,-0.8 sx <3.2 1,3.2 sx Round your answers to 3 decimal places Determine the following ) P(X 1.8)-065 b) P(X >-1.5) = c) P(X -2) exact number, no tolerance
A mixed random variable X has the cumulative distribution function e+1 (a) Find the probability density function. (b) Find P(0< X < 1).
Let X be a random variable with the following cumulative distribution function (CDF): y<0 (a) What's P(X < 2)? (b) What's P(X > 2)? c)What's P(0.5 X < 2.5)? (d) What's P(X 1)? (e) Let q be a number such that F(0.6. What's q?