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Rats are kept in = cage with tw compartments (A and B} Rats nearest Inousandth: 0.444 0.556move to with probability 0.4. Rals in Move Awith probability 0.5. Find th...

Question

Rats are kept in = cage with tw compartments (A and B} Rats nearest Inousandth: 0.444 0.556move to with probability 0.4. Rals in Move Awith probability 0.5. Find the long-term trend for rats in each compartment Round numbers0.600 0.400556 0.4440.570 0.430

Rats are kept in = cage with tw compartments (A and B} Rats nearest Inousandth: 0.444 0.556 move to with probability 0.4. Rals in Move Awith probability 0.5. Find the long-term trend for rats in each compartment Round numbers 0.600 0.400 556 0.444 0.570 0.430



Answers

Alrik’s gerbil cage has four compartments, A, B, C, and D. After careful observation, he estimates the proportion of time the gerbil spends in each compartment and constructs the table below.
$$\begin{array}{|c|c|c|c|c|}\hline \text { Compartment } & \mathrm{A} & \mathrm{B} & \mathrm{C} & \mathrm{D} \\ \hline \text { Proportion } & {0.25} & {0.20} & {0.35} & {0.30} \\ \hline\end{array}$$
(a) Is this a valid probability function? Explain.
(b) Is there a problem with Alrik’s reasoning? Explain.

So in number nine, they want to know if this is a probability distribution. So we just have to make sure that they all add up to one, because they are all between zero and one. So I'm gonna take 0.25 0.20 0.35 and 0.30 Carry one or 56789 10 11 There's not a one, not a probability distribution.

So we're given the probably density function fifties or in your group, Its power minus 0.0 to t taken very from zero to infinity. So we need to find the property that there are two learning 50 seconds or less. So need to capture the integral 0 50 50. Did he? Okay, so is approximately point 632 and two.

Okay. The probability that rat takes 1 50 seconds or less to learn is equal 2.950213 and the property there that takes more than 1 50 seconds is one minus. Probably deal that taking 1 50 seconds or less is because the event that rat takes more than 1 50 seconds to learn is the compliment for the event that the right takes 1 30 seconds or less. So this is equal to one minus 10.950213 is equal 2.0 49787

In problem 101. We have an urgent care facility in which patients arrive at an average rate of one patient every seven minutes, which means that it equals one in seven or one divided by seven. We will assume the duration between arrivals is exponentially distributed or it has an exponential distribution, which means we can now define a random variable X, which is the duration between patients arrival. And we can say that it follows an exponential distribution with the rate of one divided by seven. And, of course, the random variable is in minutes. Now we can continue to answer birds from a to D party. A. We want to find the probability that the time between two successive visits or deliberation is this than two minutes. Simply, we want to get the probability of the random variable to bill is then two minutes as they're under variable follows an exponential distribution. It means it has a community probability equals one minus E to the power of minus m are deployed by X. We're exile. Is this value then, to get the probability of the random variable to be less than two minutes, it equals one minus E is a part of minus M, where M is the red one, divided by seven multiplied by X X years too, which he gives or going to for a five for Bharti. We want to get the probability the time between two successive visits will be more than 15 minutes. We have here negative, then the probability of X to be greater than equals 15 minutes more than 15 minutes. It's somebody equals the compliment event one minus the compliment event or minus the probability of X to be smaller than 15 minutes. And this is a continuous distribution. We can add the equal sign. We can ignore it. Then it equals E to the bar of minus mm, multiplied by X. We have here M is one divided by seven and X here is 15. Then the answer is 4.1173 for birth C. We have an information about the loss to visit or the last arrived. The rest arrival has post since the minutes. We want to find the probability that the next arrival will be within the next five minutes. Then we want to get the probability for the random variable to be greater smaller than 15 minutes to happen before 15 minutes, given the random variable is greater than 10 minutes, this means the minutes husbands. The minutes have passed since the last visits, and we want to get the probability to happen within the next five minutes. After the 10 minutes using the complemented event, we can write it as one minus the probability for the random variable to be greater than 15, given that the random variable is greater than 10 using the Memories property, which says that we can really this as one, minus the probability of the random variable to be greater than the difference between these two values. 15 minus 10, which gives five again. This is a compliment event for the following. The probability of X to be smaller than five then equals using the cumulative probability function one minus. He was about, uh, minus. MX Emir is one divided by seven and X is five, which gives 4.51 46 Finally, for body, we want to find the probability that more than eight patients arrive during a half hour period. Eight patients arrived in half hour buried, which means 30 minutes and we put the random variable here in minutes and it's defined as the duration between patients arrival. Then we want to get it. Has the one interval happens at what time or what duration? We can answer this by getting assessor one multiplied by 30 divided by it. It's 30 divided by it, one multiplied by 30 divided by eight. Then we can get the probability for ex to be smaller than 30 divided by it as an adoration. If the duration is smaller than 30 divided by eight or three point 0.75 If the duration between arrivals is less than 3.75 this means more than eight patients will arrive during a half hour parrot, which equals one minus e to the power of minus one, divided by seven multiplied by X, which is here now 3.75 Then the probability equals 4.41 47 And this is the final answer of Bardi. Final answer. Barzee. Final answer of party and the final answer of party


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