(a)
P (customer order square window) = P (X= 44, Y = 44) + P (X = 48, Y= 48) = 0.05+ 0.10 = 0.15.
(b)
P (XY >= 1936) = P (X = 44, Y = 44) + P( X = 44, Y = 48) + P ( X= 48, Y=44) + P (X=48, Y=48) +P (X = 52, Y = 44) + P (X = 52, Y = 48)
= 0.05 + 0.05 + 0.15 + 0.10 + 0.30 + 0.05
= 0.70
(C)
E (X) = 44× 0.15 + 48 × 0.40 + 52 × 0.45
= 6.6 + 19.2 + 23.4
=49.2
E (Y) = 32× 0.30 + 44 × 0.50 + 48 × 0.20
= 9.6 + 22.0 + 9.6
= 41.2
E (XY) = 2028
Cov (X, Y) = E (XY) - E (X) E (Y) = 2028 - 49.2 × 41.2
= 0.96
(d) r = 0.05412
There is week Correlation.
1. Consider the joint probability distribution of window orders for a company in 2017 given the...
ka (3) [6 pts] X and Y are discrete random variables with the following joint distribution: 14 22 30 065 102 0.05 0.10 0.03 0.01 Value ofX 50.17 0.15 0.05 0.02 0.01 8 0.02 0.03 0.15 0.10 (a) Calculate the probability distribution, mean, and variance of Y (b) Calculate the prohability distribution, mea, and variane of Y given X (c) Calculate the covariance and correlation between X and Y 8
4.73 consider the joint probability distribution
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Q1. [4+2+4 marks] Consider the following joint probability distribution fxy(x, y). 2 4 0.05 0.1 0,05 0.02 0.1 0.05 2 0.02 0.13 0.3 0.01 0.02 0.15 a) Find the covariance between X and Y b) Are X and Y independent? Explain. c) Find V(X12).
Refer to the probability distribution in Section 3.1 Exercise 8
of the text above.
1) Calculate the standard deviation of the random variable.
2) Calculate the expected value for the random variable.
8. Stone Pizza Place sells 5 different sizes of round pizza. Using sales data from last year, the following table lists the diameter of pizzas sold and the corresponding probabilities that a randomly selected customer will order one of them. Diameter (inches) 10 12 14 16 18 Probability...
Q#1 Let X and Y are joint probability functions given by a- f(x, y) = *y*; x = 1, 2, 3; y = 1, 2 b- f(x,y) = 5%; x = 2,4,5; y = 1, 2, 3 Find the marginal probability functions of r.v X&Y also find out if X & Y are independent? Q#2 Let X denotes the number of times a certain numerical control machine will malfunction: 1, 2, or 3times on any given day. Let Y denote...
Please show how did you came up with the answer, show formulas
and work. Also, please do Parts e to i. Thank you so much
1. Consider the following probability mass function for the discrete joint probability distribution for random variables X and Y where the possible values for X are 0, 1, 2, and 3; and the possible values for Y are 0, 1, 2, 3, and 4. p(x,y) <0 3 0 4 0.01 0 0 0.10 0.05 0.15...
1. The following is the probability distribution of the number of customers buying bicycle accessories at a particular shop in one day. 1 4 X P(X = x) 0 0.05 2 0.15 3 0.25 5 0.30 6 0.05 0.10 a (a) (b) (c) Compute the value of a. Find the probability that the shop did not sell any bicycle accessory in one day. Find the probability that at least three customers bought from the shop in one day. Find the...
1) Consider the following distribution and random numbers: Demand Frequency 0.15 0.30 0.25 0.15 0.15 Random Numbers; 62 13 25 40 0 4 What four demand values would be developed from the random numbers listed? 2) Given the following random number ranges and the following random number sequence: 62, 13, 40, 86, 93, determine the expected average demand for the following distribution of demand. Random Demand Number Ranges 00-14 15-44 45-69 70-84 85-99 Answer:_ The number of cars arriving at...
Have to show work for every problem
4. A company uses three plants to produce a new computer chip. Plant A produces 30% of the chips. Plant B produces 45% of the chips. The rest of the chips are produced by plant C. Each plant has its own defectiv rate. These are: plant A produces 3% defective chips, plant B produces 1% defective chips, plant C produces 5% defective chips. Hint: draw a tree diagram. (a) Construct a tree diagram...