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- 2. A bucket has three marbles. Two are black and one is white. You keep drawing until you get a while marble. Every time you draw a black marble you put it back into the bucket and also add a new white marble to the bucket. The random variable X denotes the total number of marbles you have drawn from the bucket. A. Find P(X = k) as a function of k. В. Compute E(X).What does the memoryless property refer to? An event cannot occur if it has already occured within a recent specified time period. The distribution of the time until an event does not depend on how much time has already passed. The occurrence of an event is independent of the number of times that event has already occurred. None of the above. Suppose X~ GAM (a, 3). Which of the following statements are true? Select all that apply. 3 is a location parameter. E[X]=a3 a is a location parameter. 3 is a shape parameter. 3 is a scale parameter. a is a shape parameter. a is a scale parameter. For a > 1, the probability density function (pdf) is monotonic decreasing. For a < 1, the probability density function (pdf) is monotonic decreasing. None of the above.Let X denote the number of baggers on duty at a local supermarket and let Y denote the length of time (in minutes) that it takes for a customer to get through the checkout line. O A. X Y Find the significant two-tailed. O C. O D. 3 9 0.000709147 0.000707247 0.000707137 0.000707147 4 11 5 14 10 26 5 15 7 17 8 17
- 5.1.3 WP s the probability that a bit has high, moderate, and low distor- tion is 0.01, 0.04, and 0.95, respectively. Suppose that three bits vs In the transmission of digital information, are transmitted and that the amount of distortion of each bit is assumed to be independent. Let X and Y denote the number of bits with high and moderate distortion out of the three, respectively. Determine: a. fxy(x, y) b. fx(x) с. Е(X)6.1 Wse the fum fiom to find the imge of v and Hhe pieimuge of W T(v., Vx) = (v, + V, Vq x), v- (3, - 6) , w - (7,) the image of %3D O the peimage af w (if the vestor hav on nomm ber * solutiuns, jive your omsuweo in terme f pranete t. ) infinite6. Let I have a t-distribution with n degrees of freedom. Show that T² has an F- distribution with 1 and n degrees of freedom.
- Exercise 10. Suppose that A ~ N(1,4), B ~ N(-2,9), and assume that A and B are independent. (b) What is the distribution of A – B? Make sure you give the numerical values of E(A – B) and var(A – B). (c) Compute P(A > B).4.2.15 Use the data in the following table, which lists drive-thru order accuracy at popular fast food chains. Assume that orders are randomly selected from those included in the table Drive-thru Restaurant o A B D Order Accurate Order Not Accurate 335 277 235 138 34 52 38 15 If two orders are selected, find the probability that they are both accurate. Complete parts (a) and (b) below. a. Assume that the selections are made with replacement. Are the events independent? The probability is 0.7679. The events are not independent. (Do not round until the final answer. Round to four decimal places as needed.) Enter your answer in the answer box and then click Check Answer 1 part remaining Clear All search 86°F Su3. Alice and Bob buy a bag of apples, which contains 10 good and 4 bad apples. They split the apples in half evenly: Alice and Bob each take 6 apples, chosen at random. Let Agood be the number of good apples Alice gets, and define Abad, Bgood, and Bbad similarly. Describe the distribution of Agood as a hypergeometric distribution (give its parameters). Then, write Abad, Bgood, and Bbad as functions of Agood-