Consider the following discrete random variables W is the number of times heads is observed when a fair coin is tossed...
Consider the following discrete random variables
W is the number of times heads is observed when a fair
coin is tossed 10 times.
X is the number of red balls drawn when 10 balls are drawn
without replacement from an urn containing 50 red balls and 30
green balls.
Y is the number of hearts received when a 10-card hand is
dealt from a standard deck.
Z is the number of hearts drawn when 1 card is drawn at
random from each of 10 separate decks.
Which of these random variables have a Binomial distribution?
A. W only
B. Z only
C. W and Z only
D. W, Y and Z only
E. all of them
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Consider the following discrete random variables W is the number of times heads is observed when a fair coin is tossed...
a. Suppose that a fair coin is tossed 15 times. If 10 heads are observed, determine...
a. Suppose that a fair coin is tossed 15 times. If 10 heads are observed, determine an expression / equation for the probability that 7 heads occurred in the first 9 tosses. b. Now, generalize your result from part a. Now suppose that a fair coin is to be tossed n times. If x heads are observed in the n tosses, derive an expression for the probability that there were y heads observed in the first m tosses. Note the...
a coin is tossed 12 times then what is the probability at most 4 of the...
a coin is tossed 12 times then what is the probability at most 4 of the tosses are heads? what is the probability of the heads number more than 4 and less than 7? four balls are drawn at random from a box containing 2 red 2 white and 1 yellow balls what is the probability that the remaining ball is red
A fair coin is tossed 20 times. Let X be the number of heads thrown in...
A fair coin is tossed 20 times. Let X be the number of heads thrown in the first 10 tosses, and let Y be the number of heads tossed in the last 10 tosses. Find the conditional probability that X = 6, given that X + Y = 10.
A fair coin is tossed 20 times. Let X be the number of heads thrown in...
A fair coin is tossed 20 times. Let X be the number of heads thrown in the first 10 tosses, and let Y be the number of heads tossed in the last 10 tosses. Find the conditional probability that X = 6, given that X + Y = 10.
A fair coin is tossed n times. Let X be the number of heads in this...
A fair coin is tossed n times. Let X be the number of heads in this n toss. Given X = x, we generate a Poisson random variable Y with mean x. Find Var[Y]. Answer depends on n.
Suppose a fair coin is tossed 280 times. Find the probability that the number of Heads...
Suppose a fair coin is tossed 280 times. Find the probability that the number of Heads observed is 151 or more. Use Binomial Distribution and Normal Approximation and compare the results.
A fair coin is tossed 10 times and the number of heads is counted. Complete parts...
A fair coin is tossed 10 times and the number of heads is counted. Complete parts (a) through (d). a. Use the binomial distribution to find the probability of getting 5 heads. (Round to four decimal places as needed.) b. Use the binomial distribution to find the probability of getting at least 5 heads. (Round to four decimal places as needed.) c. Use the binomial distribution to find the probability of getting 5 to 7 heads. (Round to four decimal...
Let random variable x represent the number of heads when a fair coin is tossed two...
Let random variable x represent the number of heads when a fair coin is tossed two times. a) construct a table describing probability distribution b) determine the mean and standard deviation of x (round to 2 decimal places)
A coin is tossed three times. X is the random variable for the number of heads...
A coin is tossed three times. X is the random variable for the number of heads occurring. a) Construct the probability distribution for the random variable X, the number of head occurring. b) Find P(x=2). c) Find P(x³1). d) Find the mean and the standard deviation of the probability distribution for the random variable X, the number of heads occurring.
A fair coin is tossed 21 times. What is the probability that at most 18 heads occur? a) 0.0006341...
A fair coin is tossed 21 times. What is the probability that at most 18 heads occur? a) 0.00063419 b) 0.01074482 c) 0.99988937 d) 0.99925518 e) 0.00011063 An urn contains 11 white balls and 9 green balls. A sample of seven is selected at random. What is the probability that the sample contains at least one green ball? a) 0.946362 b) 0.995743 c) 0.999884 d) 0.053638 e) 0.000116 A classroom of children has 10 boys and 16 girls in which...
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