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Find the expected value (mean), variance, and standard deviation for
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Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
- Suppose that the probability that a patient admitted in a hospital is diagnosed with a certain type of cancer is 0.03. Suppose that on a given day io patients are admitted and X denotes the number of patients diagnosed with this type of cancer. The mean and the variance of X are: E(X)=0.4 and V(X)=0.384 O None of these O E(X)=0.5 and V(X)=0.475 O E(X)=0.3 and V(X)=0.291arrow_forwardE and F are independent variables with variances of 7 and 9, respectively. Given this, Var(2E - F + 2) = ? Show complete solution.arrow_forward8 Show that E { X – m3 = E(X)³- 3m of-m, where m and of are the mean and variance of X respectively. %3Darrow_forward
- The mean is equal to of cellular phones of sold per day is therefore, it means that the average number To find the variance complete the table below: P(x) x2 - P(x) .2 X•P(x) 15 0.30 4.5 18 0.20 3.6 19 0.20 3.8 20 0.15 22 0.15 3.3 ix2 . P(x) = g? = ) [x² · P(x)] - u² = %3D %3D %3D while herefore, the variance of a probability distribution is equal to ne standard deviation is equal to such a igher ngarrow_forwardLet X have a mean of 132 and a variance of 32. Define Y = X² + 2X + 1. Compute the (a) mean and (b) variance of Y. (a) i (b) iarrow_forwardFind the mean m = E(X), variance o; = var(X), and standard deviationo = Ox of each distribution: %3| %3D %3D 2 3 11 1 3. 4 (a) f(x) 1/3 1/2 1/6 (b) f(x) 0.4 0.1 0.2 0.3 Use the formulas, µ = E(X) = x, f (x) + x2f (x) + ... + xmf (x) = * f(x) + Xm f (Xm) = _x,f (x) %3D E(X³) = x{f(x) + x3f(x) +...+ x(xm) = f(x) %3D Then use the formulas = var (X) = E(X²) – µ² and o = 0x = var(X). %3Darrow_forward
- Suppose it is desired to estimate the variance of the tensile strength of a particular type of thread. For 21 pieces of this type of thread, E(X; - Xave)² = 2000. What is the point estimte of the true standard deviation of the tensile strength of this thread?arrow_forwardAssume that X is normally distributed with a mean of 10 and a standard deviation of 2. Determine the value for x that solves each of the following: a P(X > x) = 0.5 b P(X > x) = 0.95 c P(x < X < 10) = 0 d P(-x < X - 10 < x) = 0.95 e P(-x < X - 10 < x) = 0.99arrow_forwardIf X N(49, 16), then the standard deviation of X equalsarrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill