Suppose E(X) = 5 and EIX(X-1)] = 27.5. What is
a. E(X)? [Hint: E[X(X - 1)] = E[X² - X] =
E(X²) - E(X)]?
b. V(X)?
c. The general relationship among the quantities E(X), EIX(X-1)], and V(X)?
Compute the following binomial probabilities directly from the formula for b(x; n, p): b. b(5; 8, .6)
a. b(3: 8..35)
c. P(3 ≤X ≤ 5) when n = 7 and p = .6 d. P(1X) when n = 9 and p = 1
Let X, the number of flaws on the surface of a randomly selected boiler of a certain type, have a Poisson distribution with parameter µ = 5. Use Appendix Table A.2 to compute the following probabilities: a. P(X ≤ 8) b. P(X = 8) c. P(9 ≤ X)
d. P(5 ≤X ≤ 8) e. P(5 < X < 8)
There are two machines available for cutting corks intended
for use in wine bottles. The first produces corks with diam
eters that are normally distributed with mean 3 cm and stan
dard deviation .1 cm. The second machine produces corks
with diameters that have a normal distribution with mean
3.04 cm and standard deviation .02 cm. Acceptable corks
have diameters between 2.9 cm and 3.1 cm. Which machine
is more likely to produce an acceptable cork?
Let X denote the number of flaws along a 100-m reel of magnetic tape (an integer-valued variable). Suppose X has approximately a normal distribution with = 25 and a = 5. Use the continuity correction to calculate the prob ability that the number of flaws is a. Between 20 and 30, inclusive.
b. At most 30. Less than 30.
describe the direction that the authorities should follow in order to reverse the continually deepening economic stagnation in South Africa?
The Toyota Motor Corporation makes cars in response to customer orders rather than attempting to sell cars it has already built. If the company received a large increase in orders for its Prius model, what will be expected of its current supply curve on a demand and supply diagram?
1. difference(s) between the classical and Keynesian aggregate demand schedules. In your explanation indicate what factors shift aggregate demand in the classical model and Keynesian model? (4)
What is the key difference between the classical and Keynesian aggregate supply functions? What are the key factors that drive these differences? (4
Instructions that help match one person's saving with another person's investment are collectively called?