Determine the following probabilities:
X -2 -1 0 1 2
f(x) 0.125 0.25 0 .25 0.25 0.125
PX<=2)
P(X> -2)
P(-1<= X,<= 1)
P(X<- -1)
Suppose that f (x) = 1.5X2 for -1 < X < 1 . Determine the following probabilities a) p(0<X) = 0.5 b) P(0.6< X)0.284 c) P(-0.5sX 0.5) = 0.125 (Round the answer to 3 decimal places.) Round the answer to 3 decimal places.) f) Determine x such that P(x < = 0.05 Round the answer to 3 decimal places.)
Suppose that f(x) - or 0<X<8 256 Determine the following probabilities. Round your answers to 3 decimal places (e.g. 98.765) (a) P(X < 2)=7456 (b) P(X< 9) = (d) P(X > 5)- 316 (e) Determine such that P(x x)-0.90 X6.302
Suppose that f(x) = e-x for x > 0. Determine the following probabilities: Round your answers to 4 decimal places. a) P(X=3)
4-1. Suppose that f(x)-e-x for 0 < x. Determine the fol- lowing probabilities: (c) P(X= 3) (e) P(3 s x) (d) P(X<4)
Question 1) Consider the following Cascade of two Binary symmetric channels (CBSC) with probabilities as indicated in the figure below 1. Find P(Y=1 / X=1 ), P(Y=0 / X=1) 2. Find P(Y=1 / X=0 ), P(Y=0 / X=0) 3. Find The Channel Matrix for each BSC separately 4. Find The overall Channel Matrix of the cascade channels 5. Assume that P1 = P2 = Pe , Prove that the Channel Matrix is M2 6. Use the assumptions and results in...
Given that f(x) = e-(x-1) for x > 1, determine the following probabilities: a) P(X < 4), b) P(X > 3.5), c) P(4 < X < 5), d) P(X < 4.5), e) P(X < 3.5 or X > 4.5)
6. Suppose that X and Y have a bivariate normal distribution with px 1 and y- (a) Order the following probabilities from largest to smallest, assuming p >0: P(X 2 (b) Repeat (a) assuming p < 0. (c) Repeat (a) assuming we are interested in (X 0.25) instead of (x 2 2). 6. Suppose that X and Y have a bivariate normal distribution with px 1 and y- (a) Order the following probabilities from largest to smallest, assuming p >0:...
x P(x) 0 0.125 1 0.375 2 0.375 3 0.125 Use the following table to determine whether or not a probability distribution is given. If a probability is given, find its mean and standard deviation.
Consider a random variable X, that takes values 0 and 1 with probabilities P(0) = P(1) = 0.5. Then, X = 0 with probability 0.5 and X = 1 with probability 0.5. What is the expected value of X? 0 0.25 0.5 1
1) Binomial distribution, f(x) = px (1 – p) n-x , x = 0, 1, 2, …, n n = 10, p = 0.5, find Probabilities a) P(X ≥ 2) b) P(X ≤ 9) 2) f(x) = (2x + 1)/25, x = 0, 1, 2, 3, 4 a) P(X = 4) b) P(X ≥ 2) c) P(X ≥ -3) 3) Z has std normal distribution, find z a) P(-1.24 < Z < z) = 0.8 b) P(-z < Z <...