A random variable has the following distribution
X |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
P(x) |
k |
3k |
5k |
7k |
9k |
11k |
13k |
15k |
17k |
A random variable has the following distribution X 0 1 2 3 4 5 6 7...
X = o,1,2,3 and P(X)= 2k,3k,13k,2k. how is this problem done? a random variable X has a probability distribution as follows done? What is K and why is its value .05 Total probability = 1 2k+3k+13k+2k= 1 k= .05 p(x<2)= 2k + 3k = 5k = 5*.05=.25 Answer is B 0.25
2.1 Let X be a discrete random variable with the following probability distribution Xi 0 2 4 6 7 P(X = xi) 0.15 0.2 0.1 0.25 0.3 a) find P(X = 2 given that X < 5) b) if Y = (2 - X)2 , i. Construct the probability distribution of Y. ii. Find the expected value of Y iii. Find the variance of Y
The following table shows the probability distribution of a random variable X 2 -2 -1 0 1 х с f(x) 2k k 3k 0.3 0.1 It is given that E(5X 2) 3; (a) Find c and k; (4
5. Suppose X is a discrete random variable that has a geometric distribution with p= 1. a. Compute P(X > 6). [5] b. Use Markov's Inequality to estimate P(X> 6). [5] c. Use Chebyshev's Inequality to estimate P(X>6). [5] t> 0 6. Let be the probability density function of the continuous 0 t< 0 random variable X. a. Verify that g(t) is indeed a probability density function. [8] b. Find the median of X, i.e. the number m such that...
4. A mixed random variable X has the cumulative distribution function: (0. for x < 0.4 X2 – 0.02 for 0.4 < x < 0.5 Fx(xx) = { 0.2.x3 + 0.6x + 0.25 for 0.5 < x < 0.7 for x > 0.7 (a) Calculate the mean and standard deviation of X. (b) Find P(0.44 < X < 0.62).
The random variable X takes the values -2, -1 and 3 according to the following probability distribution: -2 3k -1 2k 3 3k px(x) i. Explain why k = 0.125 and write down the probability distribution of X. ii. Find E(X), the expected value of X. iii. Find Var(X), the variance of X.
Suppose that the random variable X has the discrete uniform distribution f(x) = { 1/4, r= 5, 6, 7, 8. 0, otherwise. A random sample of n = 45 is selected from this distribution. Find the probability that the sample mean is greater than 6.7. Round your answer to two decimal places (e.g. 98.76). P= the absolute tolerance is +/-0.01
6. The distribution law of random variable X is given -0.4 -0.2 0 0.1 0.4 0.3 0.2 0.6 Xi Pi Find the variance of random variable X. 7. Let X be a continuous random variable whose probability density function is: f(x)=Ice + ax, ifXE (0,1) if x ¢ (0:1) 0, Find 1) the coefficient a; 2) P(O.5 X<0.7); 3) P(X>3). Part 3. Statistics A sample of measurements is given Y 8 4 2 2 0 8. Compute the coefficient of...
The random variable X has the probability distribution table shown below. x 2 4 6 8 10 P(X = x) 0.2 0.2 a a 0.2 (a) Assuming P(X = 6) = P(X = 8), find each of the missing values. a = (b) Calculate P(X ≥ 6) and P(2 < X < 8). P(X ≥ 6) = P(2 < X < 8) =
3. The probability distribution of the discrete random variable X is f(x) = 2 x 1 8 x 7 8 2−x , x = 0, 1, 2. Find the mean of X. 4. The random variable X, representing the number of errors per 100 lines of software code, has the following probability distribution: x 1 2 3 5 6 f(x) 0.03 0.37 0.2 0.25 0.15 (a) Find E(X). (b) Find E(X2 ). 5. Use the distribution from Problem 4. (a)...