Suppose X is a random variable and Y is not a random variable. What kind of vari

Question

Suppose X is a random variable and Y is not a random variable. What kind of variable (random or not random) is W when a. W = X + Y b. W = XY c. W = 2Y d. W = X^2 Calculators produced by a manufacturer were of poor quality, and a shipment with 300 calculators had 40% defective. (a) What is the probability that two randomly drawn calculators from this shipment are both defective? (b) After tightening up quality control, this figure was reduced to 10% defective. A shipment with 900 calculators was sent. Repeat (a) for this shipment. (c) A calculator from one of the two shipments was tested, and it was defective. What was the chance it was drawn from the second shipment?

Explanation / Answer

4) In a,b,d ; variable is random cause depends on X which itself is random. While in c it is not random cause depends only on non random variable

5)

a)here number of defective =300*40%=120

therefore probability that both are defective =(120/300)*(119/299)=0.159197

b)

here number of defective =900*10%=90

therefore probability that both are defective =(90/900)*(89/899)=0.0099

c) probability that it was defective =P(D) =from 1st shipment and defective+from 2nd shipment and defective

=P(1)*(D|1)+P(2)*P(D|2) =(300/1200)*0.4+(900/1200)*0.1=0.175

hence probability it is from second shipment given defective =P(2|D) =P(2)*P(D|2)/P(D)

=(900/1200)*0.1/0.175=0.428571

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