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Graph the probability. P [Z=1.5]...

Question

Graph the probability. P [Z=1.5]

Graph the probability. P [Z=1.5]



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Sketch a graph of the probability distribution and find the required probabilities. $$ \begin{array}{l}{\text { (a) } P(x \leq 2)} \\ {\text { (b) } P(x>2)}\end{array} $$

In the current problem, their students. So we have to find out, Uh, what would be the distribution off problem? Uh, diagram of distribution. Off probability. So what do we understand By probably distribution. We understand that the variable eggs can have these values in which we can think this'll Toby like, out of 1000 times, 27 times it will become zero 1 89 approximately. It will take the value one. Okay, 4, 41 times. It will be the value to on 3. 43 times approximately. It will take the value three. So now, if we go ahead on, try toe, verify if this is a probable to distribution or not. First, we should validate the basic formulas, not formulas. The conditions that would be zero less cynical. Soupy X less than one. That means to be a positive quantity. These all are positive quantity, and all are less than one. So it's the first condition is verified. The second one would be to check summation off PX. Easy equals to one. All right, so we will check the addition. So that's why we have already kept the numbers ready here. So nine plus one tin on seven plus 3. 10, 10, 10 plus 10. 20. So we get a zero over here on a two over here. No. Eight plus 2, 10 and four plus 48 plus two again. 10, 13, plus 10. 20 again and zero. So we get another carry forward now. Four plus +37 plus +18 plus 2 10. So we get a zero here, and then we get the carry forward one here. So, yes, the total probability is one. Now we have to draw the diagram. So there are horizontal axis. We plot the X variable on in the vertical axis. We will be putting the properties. So if we take five small units, small sides of the boxes to represent the probability is the 0.1 the same way. If we go ahead. So 12345 We get over here. 0.2 on the same line we will be getting 12345 Be good. 0.3 on then on the same line. 0.4 and then zero point fake. Now it's clearly impossible for us human beings to behave like computers, isn't it? So we will think off approximate values. You can think this can be approximated to 0.3 which is very, very much nearby here. Now, what is this distance? That total distance is 0.1. So 0.1. If it is divided by two, it will get 0.50 point 03 is even lesser than 0.5. So we can think somewhere over here it should be so. We plot for zero. This is the probability to be Draw a straight line. And this is the problem for zero now. For one, it is 0.189 So what is 0.189? It could be rounded off to zero point toe near about. So we get over here, but a little less than that. So hence somewhere in there minted and then 0.441 We can think of it like something about 0.4, but little up than that. So it will be little Upton that so somewhere over here? Okay on. Then we get for X equals 230.3 for three with you can think like 0.35 So it's 0.3 and then halfway through. So it should be somewhere over here. So now the final touch would be toe have the straight lines, which would be from here I draw like this on. Then again from here to hydraulic this on then from helps. Um, from here, draw like this. So that's how the probability distribution looks like for ex. Now we have to find the probability off X line between between one and two. So first one is probability off one listen equals two X listen equals to two. That means it can be this and this this region off course, it will be probability off one plus probability. Off to what is the probability? Off one, It's 0.189 plus what is the probability of 20.441? So it will be nine plus one, Cyril nine plus four. It's three on one more. So it is 60.630 Correct. So now the other part of this question is property off X, less than equals to two ops less than two. So the question is probability X less than toe, not equal. So what are the values off X, which are less than two. So it's one and zero. The probability of zero less probability off one. What is the probability of zero? It's zero point 0 to 7. So right, 0.27 and the other part being zero point 189 So we add this too. So we get six and then fun on then, too. So we get 0.216 So this on this side, the answers, I hope that's simple enough.

This time they want us to find the well. You. They want us to find the expected value, Uh, given probability distribution in the history room. Okay. I ran a variables X. And they tell us when we interpret that Mr Graham, that one occurs with a point to her ability. 2/10 of the time the value of two occurs. Three hunts of the time about you. Three Kurds. One about you for kers, for attempts of the time. Okay. So we can compete. Be careful, willing get zero to value zero point in the second. Another 0.3 on one point and then we this value points.

It is. They give us a probability distribution from a history and they want us to compete. He expected, will you? We're in the variable, and I see that the value to occurs to tens of the time value for occurs three times sometime. The value occurs to tens of the time. The value eight occurs 1/10 of on the value term occurs sense of the time. So we, the mosque that are expected value for a single given trial would be 5.6.

This time they give us another probability in the form of Instagram so he can read, though a value of six will occur. Zero plane 1% of the time. So 1/10 of with him value. 12 will occurred to 10. The value. 18 Julia Kurds for tens of the time. The value. 24. Here's to tens of the time the value of 30. There's 1/10 of the time we'll compete that we'll actually see that the average value tell you traditional in trial baiting.


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