Question

In: Math

Let the probability of success on a Bernoulli trial be 0.20. a. In nine Bernoulli trials,...

Let the probability of success on a Bernoulli trial be 0.20. a. In nine Bernoulli trials, what is the probability that there will be 8 failures? (Round your final answers to 4 decimal places.) Probability b. In nine Bernoulli trials, what is the probability that there will be more than the expected number of failures? (Round your final answers to 4 decimal places.) Probability

Solutions

Expert Solution

p=probability of success in a Bernoulli trial=0.2

q=1-p=probability of success in a Bernoulli trial=1-0.2=0.8

Let X= number of failures in 9 Bernoulli Trials

1)

The probability that there will be 8 failures in 9 Bernoulli trials =P(X=8)

2)

Expected number of failures= E(X)= n* q= 9*0.8=7.2 ( formula for the expectation of Binomial distribution)

Hence, the probability that there will be more than the expected number of failures in 9 Bernoulli trials=P(X>7.2)=P(X>=8)

( Because X can take only integer values, Being a discrete distribution)


Related Solutions

Shown below are the number of trials and success probability for some Bernoulli trials. Let X...
Shown below are the number of trials and success probability for some Bernoulli trials. Let X denote the total number of successes. n = 6 and p = 0.3 Determine ​P(x=4​) using the binomial probability formula. b. Determine ​P(X=4​) using a table of binomial probabilities. Compare this answer to part​ (a).
. In a sequence of 7 Bernoulli trials with probability of success p, let X be...
. In a sequence of 7 Bernoulli trials with probability of success p, let X be the number of successes not followed immediately by a failure. Find E(X) (you can use indicators)
Negative Binomial experiment is based on sequences of Bernoulli trials with probability of success p. Let...
Negative Binomial experiment is based on sequences of Bernoulli trials with probability of success p. Let x+m be the number of trials to achieve m successes, and then x has a negative binomial distribution. In summary, negative binomial distribution has the following properties Each trial can result in just two possible outcomes. One is called a success and the other is called a failure. The trials are independent The probability of success, denoted by p, is the same on every...
Suppose 4 Bernoulli trials, each with success probability p, are conducted such that the outcomes of...
Suppose 4 Bernoulli trials, each with success probability p, are conducted such that the outcomes of the 4 experiments are mutually independent. Let the random variable X be the total number of successes over the 4 Bernoulli trials. (a) Write down the sample space for the experiment consisting of 4 Bernoulli trials (the sample space is all possible sequences of length 4 of successes and failures you may use the symbols S and F). (b) Give the support (range) X...
Provided a standard sequence of n independent Bernoulli trials in which the probability of success is...
Provided a standard sequence of n independent Bernoulli trials in which the probability of success is θ and the probability of failure is 1−θ. If A represents the observed number of success and B represents the observed number of failures, (with A+B = n), then find I(θ), the Fisher information matrix. (Hint: Recall that the sum of n Bernoulli trials is a Binomial random variable. Also assume that n, A and B are fixed and so the only unknown parameter...
Consider a binomial experiment with 20 trials and probability 0.35 of success on a single trial....
Consider a binomial experiment with 20 trials and probability 0.35 of success on a single trial. (a) Use the binomial distribution to find the probability of exactly 10 successes. (Round your answer to three decimal places.) (b) Use the normal distribution to approximate the probability of exactly 10 successes. (Round your answer to three decimal places.) (c) Compare the results of parts (a) and (b). These results are fairly different. These results are almost exactly the same.
Consider a binomial experiment with 15 trials and probability 0.55 of success on a single trial....
Consider a binomial experiment with 15 trials and probability 0.55 of success on a single trial. (a) Use the binomial distribution to find the probability of exactly 10 successes. (Round your answer to three decimal places.) (b) Use the normal distribution to approximate the probability of exactly 10 successes. (Round your answer to three decimal places.) (c) Compare the results of parts (a) and (b). These results are fairly different.These results are almost exactly the same.  
Consider a binomial experiment with 16 trials and probability 0.60 of success on a single trial....
Consider a binomial experiment with 16 trials and probability 0.60 of success on a single trial. (a) Use the binomial distribution to find the probability of exactly 10 successes. (b) Use the normal distribution to approximate the probability of exactly 10 successes. (c) Compare the results of parts (a) and (b).
Let N be a binomial random variable with n = 2 trials and success probability p...
Let N be a binomial random variable with n = 2 trials and success probability p = 0.5. Let X and Y be uniform random variables on [0, 1] and that X, Y, N are mutually independent. Find the probability density function for Z = NXY . Hint: Find P(Z ≤ z) for z ∈ [0, 1] by conditioning on the value of N ∈ {0, 1, 2}.
Independent trials, each of which is a success with probability p, are successively performed. Let X...
Independent trials, each of which is a success with probability p, are successively performed. Let X denote the first trial resulting in a success. That is, X will equal k if the first k −1 trials are all failures and the kth a success. X is called a Geometric random variable (google it). Determine the moment generating function of X.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT