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borishaifa [10]
3 years ago
7

Jason Bourne has been held captive in a prison from which there are three possible routes to escape: an air duct, a sewer pipe a

nd the door (which happens to be unlocked). The air duct leads him on a three hour trip whereupon he falls through a trap door onto his head. The sewer pipe is similar but takes two hours to traverse. Each fall produces amnesia and he is returned to the cell immediately after each fall. Assume that he always immediately chooses one of the three exits from the cell with probability 1 3 . On average, how long does it take before he opens the unlocked door and escapes
Mathematics
1 answer:
laila [671]3 years ago
7 0

Answer:

  • Rx2e-xdx=-e-x(x2+2x+2)+candR-xe-xdx=xe-x+e-x+c)CS 70, Summer 2016, HW 62

Step-by-step explanation:

  • CIA(8 points)Jason Bourne has been held captive in a prison from which there are three possible routes to escape:an air duct, a sewer pipe and the door (which happens to be unlocked). The air duct leads him on athree hour trip whereupon he falls through a trap door onto his head. The sewer pipe is similar buttakes two hours to traverse. Each fall produces amnesia and he is returned to the cell immediatelyafter each fall. Assume that he always immediately chooses one of the three exits from the cell withprobability13. On average, how long does it take before he opens the unlocked door and escapes?9.Markov Chain(12 points: 4/3/5)Consider the Markov chainX(n)with the state diagram shown below, wherea,b∈(0,1).Figure 1: State diagram(a) Is this Markov chain irreducible? Is it aperiodic? Briefly justify your answers.(b) Calculate Pr[X1=1,X2=0,X3=0,X4=1|X0=0].(c) Calculate the invariant distribution.CS 70, Summer 2016, HW 63
  • Alice and Bob are going to study for the upcoming midterm together. They agree to meet at timetthis afternoon. Alice will show upXhours aftert, whereX∈Uniform[0,2]. Bob’s arrival time ismore unpredictable. He will be distracted by Pokemon Go and will show upYhours aftert, whereY∈Expo(1). The person who shows up later is late forThours. What isE[T]? (Hint: some usefulintegrals

# if you need any queshtions aswered speedly hit me up and I got you

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Consider the probability that at least 88 out of 153 registered voters will vote in the presidential election. Assume the probab
Liono4ka [1.6K]

Answer:

0.9319 = 93.19% probability that at least 88 out of 153 registered voters will vote in the presidential election.

Step-by-step explanation:

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, using the expected value and the standard deviation.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution

Problems of normally distributed distributions can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

When we are approximating a binomial distribution to a normal one, we have that \mu = E(X), \sigma = \sqrt{V(X)}.

153 voters:

This means that n = 153

Assume the probability that a given registered voter will vote in the presidential election is 63%.

This means that p = 0.63

Mean and standard deviation:

\mu = E(X) = np = 153(0.63) = 96.39

\sigma = \sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{153*0.63*0.37} = 5.97

Consider the probability that at least 88 out of 153 registered voters will vote in the presidential election.

Using continuity correction, this is: P(X \geq 88 - 0.5) = P(X \geq 87.5), which is 1 subtracted by the p-value of Z when X = 87.5.

Z = \frac{X - \mu}{\sigma}

Z = \frac{87.5 - 96.39}{5.97}

Z = -1.49

Z = -1.49 has a p-value of 0.0681.

1 - 0.0681 = 0.9319

0.9319 = 93.19% probability that at least 88 out of 153 registered voters will vote in the presidential election.

5 0
2 years ago
Find a quadratic equation with integer coefficient ,if one of the roots is 7-root3
solmaris [256]
One of the roots of a quadratic equation is 7 - √3.

Because rational roots occur in conjugate pairs, the other root is 7 + √3.
The quadratic equation is
(x -(7-√3))(x - (7+√3))
= x² - (7+√3)x  - (7-√3)x + (49-3)
= x² - 7x - (√3)x - 7x + (√3)x + 46
= x² - 14x + 46

Answer: x² - 14x + 46


6 0
2 years ago
Find the value of x such that the data set has the given mean. 102, 119, 107, 115, 110, x; mean 117
Rufina [12.5K]

Answer:

702

Step-by-step explanation:

the answer is 702. you add all if the numbers and divide them by hiw many there are which

5 0
3 years ago
Stephen Gather data about the average rainfall in two cities who organizes data in the given
lana66690 [7]

Answer:

stephen???? not enough detail

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
2. Gerald was given the following problem to solve for the length of the "?". He has made a mistake in his work.
Degger [83]

Answer:

x = 18.7

Step-by-step explanation:

Gerald's answer is almost correct.  

He just needs to switch the 14 and the x.

it should be

24/x = 18/14

solve for x by cross multiplication

18x = (24)(14)

18x = 336

x = 18.7

5 0
2 years ago
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