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1. A woman launches a boat from one shore of a straight river and wants to land at the point directly on the opposite shore. If the speed of the boat (relative to the water) is 10 mi/h and the river is flowing east at the rate of 5 mi/h, in what direction should she head the boat in order to arrive at the desired landing point?
The probabilities of a machine manufacturing 0, 1, 2, 3, 4, or 5 defective parts in one day are 0.75, 0.17, 0.04, 0.025, 0.01, and 0.005, respectively. Find the mean of the probability distribution.
(3a-5)(9a2+25)(3a+5)
Suppose three test kits are tested at random. Let D represent the defective test kit and let N represent the non-defective test kit. If we let X be the tendon variable for the number of defective test kits, construct the probability distribution of the random variable X
Let G be a finite group.let S={g€G|g^5=e}, where e is identity element of G.show that |S| is odd.
1. The weight of Group 1:Jay - 43 kg, Stella - 42 kg, Tilly - 44 kg, Joanna - 53 kg. Consider samples of size 3 that can be drawn from this population.
a. How many possible samples can be drawn?
b. List all the possible samples and the corresponding means.
c. Construct the sampling distribution of the sample means.
Suppose a, b, c, d have proper positions 1, 2, 3, 4 respectively, i.e., the cor-
rect sequence (from position 1 to 4) is a, b, c, d. Write down all the deranged
sequences. What is the combinatorial expression for their count?
For each of the ff. sets, determine whether 2 is an element of that set.
- {{2},{2,{2}}}
- {{{2}}}
Determine whether the distribution represents a probability distribution. Explain your answer.
X
1
3
5
7
P(X)
0.35
0.25
0.22
0.12
Find Elementary matrices E1, E2 so that E2 E1 A = I2, where A = matrix(1 0 2 3) and I2 is the respective identity matrix
