X 0 1 2
f(x) 0.2 0.4 ?
1) What is the mean number of cars a family owns E(X)?
2) What is the variance of the number of cars a family owns, Var(X) = σ x^2
3) What is the standard deviation of X, sd(X) = σ x?
Let the random variable x represent the number of cars owned by a family. Assume that x can take on five values: 0, 1, 2, 3, 4. A partial probability distribution is shown below: x 0 1 2 3 4 p(x) 0.2 0.1 0.3 ? 0.1 i. The probability that a family owns three cars equals _______ ii. The probability that a family owns between 1 and 3 cars, inclusive, equals _______ iii. ...
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)...
x P(x) 0 0.25 1 0.2 2 0.15 3 0.4 Find the standard deviation of this probability distribution. Give your answer to at least 2 decimal places
Xew) 0.8 F 0.6 Consider -0.2 -1 -0.8 -0.6 -0.4 -0. 2 0 0.2 0.4 0.6 0.8 w (x21) the following plot of X(ew. Calibrate the frequency axis to the true (analog) frequency N = Fow if the sampling rate used was F, = 500Hz.
Problem 3) In an experiment to monitor two calls, the PMF of N, the number of voice calls, is 0.2 = 0 P. ) 10.7 = 1 10.1 O = 2 otherwise a) Find E[M], the expected number of voice calls. b) Find E[N], the second moment of N. c) Find Var[M, the variance of N. d) Find on, the standard deviation of N. Problem 4) For the following random variable X. 0 <-3 0.4 -35x<5 F (x)= 0.8 55x<7...
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...
. Consider the following data: Values of X 0 2 6 8 12 12 Associated probabilities P(x) 0.1 0.2 0.4 0.2 0.1 Find the expected value , E(X), that is μΧ 5 6 a) Note E (X) Σ XP(X) b) Find the variance of X, that is, ox Note Var(X): σ/ E(X2) -μα2 Where E(X) X P(X)
Consider the following data table: 0 2i = 0.2 0.4 f(xi) = 2 2.018 2.104 2.306 0.6 0.2 and 23=0.4 is The linear Lagrange interpolator L1,1 (2) used to linearly interpolate between data points 12 (Chop after 2 decimal places) None of the above. -2.50x+0.20 -5.00x+2.00 -5.00x+2.00 5.00x-1.00 Consider the following data table: 2 Ti = 0 0.2 0.4 0.6 f(x) = 2.018 2.104 2.306 0.2 and 23 = 0.4, the value obtained at 2=0.3 is Using Lagrange linear interpolation...
Consider a binomial experiment with n-12 and p 0.2. a. Compute f (0) (to 4 decimals). f(0) b. Compute f(8) (to 4 decimals) f(8) C. Compute P(z 〈 2) (to 4 decimals). d. Compute P(x 2 1) (to 4 decimals). P( 21) e. Compute E(x) (to 1 decimal) E(x) f. Compute Var(z) and σ. Var(x) - (to 2 decimals) (to 2 decimals)
Suppose the c.d.f. of X is F(t) 3 for 0<t< (a) What is F(5)? (b) What is F(-5)? (c) Compute the p.d.f of X. (d) Compute the mean of X (e) Compute the variance of X. (f) Compute the standard deviation of X (g) Compute the squared coefficient of variation of X.