The following probability mass function is considered: P(X = x) = 3x+1 x = 1, 2,...
Verify that the following function is a probability mass function, and determine the requested probabilities. f(x) = (3x+4)/50, x = 0, 1, 2, 3, 4 Is the function a probability mass function? (yes/no) Give exact answers in form of fraction. (a) P(X = 4) = ? (b) P(X ≤ 1) = ? (c) P(2 ≤ X < 4) = ? (d) P(X > -10) = ?
12
Verify that the following function is a probability mass function, and determine the requested probabilities. [Give exact answers in form of fraction.] f(x)-(5/6)(1/6)" x=0,1,2, , (a) P(X= 2) (b) P(X s 2)-.uI = i (c) P(X > 2)= (d) P(X21) = T Your answer is partially correct. Try again. Verify that the following function is a probability mass function, and determine the requested probabilities f (x)3x+3 45x 0, 1, 2,3,4 Is the function a probability mass function? Give exact...
4. Suppose that X is a random variable having the following probability distri- bution function - 0 if r<1 1/2 if 1 x <3 1 if z 2 6 (a) Find the probability mass function of X. (b) Find the mathematical expectation and the variance of X (c) Find P(4 X < 6) and P(1 < X < 6). (d) Find E(3x -6X2) and Var(3X-4).
If you only need to calculate the probability of something like P(3X+2<5) or P(X2<8) you do not need to find the full distribution of the transformed random variable. Instead you can isolate the random variable X inside the probability and perform the calculation using the distribution function of X. You must be careful if you are dealing with a non-one-to one transform (like X ). calculate these probabilities. X is a Gaussian random variable with p = 1 and a...
2. The random variable, X has the following probability mass function (i) Find the value of the constant c. HINT: It will help to use the identity = (i) Find the cumulative distribution function of X and sketch both the probability mass function and the cumulative distribution function NOTE: Think carefully about the values of r for which you need to define the distribution function. (ii) Calculate P(X 2 50) and PX 2 50 x2 40
5. Consider the discrete random variable X with probability mass function p.) = (3/30 for r=1 6/30 for r= 2 8/30 for r=3 7/30 for r = 4 4/30 for r = 5 2/30 for r= 6 10 otherwise. You may find it helpful to use a table with columns for I, Px(), 2. Px(2), and r.Px() to keep track of your computations. Do not round off-express all values as rational fractions. a) Find the probability P(X<3. b) Find the...
A discrete random variable X has the following probability mass function: p(2) DETİ, for x EA; and zero otherwise. 2 T where C is a constant and A is the support of the distribution. Find the value of C if (c) A 12,3,4,5,...) (a) A (0,2,4,6,..
A discrete random variable X has the following probability mass function: p(2) DETİ, for x EA; and zero otherwise. 2 T where C is a constant and A is the support of the distribution....
Let X ? Geometric(p) with probability mass function P(X =x)=p(1?p)x?1, x?N. (a) Verify that FX (x) = 1 ? (1 ? p)x, x ? {1, 2, 3, . . .}. (b) Graph FX(x) for x ? [?1,4] for p = 1/4. (c) Let X ?Geometric(1/4). Find P(X ? (3, 5]) and P(X is even).
Exercise 3.1. Let X have possible values {1,2,3,4,5} and probability mass function x 1 2 3 4 5 pX(x) 1/7 1/14 3/14 2/7 2/7 (a) Calculate P(X ≤ 3). (b) Calculate P(X < 3). (c) Calculate P(X < 4.12|X > 1.638).
Question 1. A Discrete Distribution - PME Verify that p(x) is a probability mass function (pmf) and calculate the following for a random variable X with this pmf 1.25 1.5 | 1.7522.45 p(x) 0.25 0.35 0.1 0.150.15 (a) P(X S 2) (b) P(X 1.65) (c) P(X = 1.5) (d) P(X<1.3 or X 221) e) The mean (f) The variance. (g) Sketch the cumulative distribution function (edf). Note that it exhibits jumps and is a right continuous function.