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1Define the probability density of the events Xi and Xz as:0.00 0.150.30 0.150.20 0.100.10 0.00(a) Calculate (i) Pr(X; > 2|X,=I) and (ii) Pr(Xz=I X, >2) . (b)...

Question

1Define the probability density of the events Xi and Xz as:0.00 0.150.30 0.150.20 0.100.10 0.00(a) Calculate (i) Pr(X; > 2|X,=I) and (ii) Pr(Xz=I X, >2) . (b) Calculate Pr( X, Xz = 0) and (ii) Pr(X; + X, > 4) (c) A random sample of 2 is taken from the variable Xi write out the jointprobability distribution of these two random variables_ (d) Write out the probability distribution of the sample mean from the random sample of 2 obtained in (c)

1Define the probability density of the events Xi and Xz as: 0.00 0.15 0.30 0.15 0.20 0.10 0.10 0.00 (a) Calculate (i) Pr(X; > 2|X,=I) and (ii) Pr(Xz=I X, >2) . (b) Calculate Pr( X, Xz = 0) and (ii) Pr(X; + X, > 4) (c) A random sample of 2 is taken from the variable Xi write out the jointprobability distribution of these two random variables_ (d) Write out the probability distribution of the sample mean from the random sample of 2 obtained in (c)



Answers

A discrete probability distribution for a random variable $\bar{X}$ is given. Use the given distribution to find $(a)$ $P(X \geq 2)$ and $(b) E(X)$. $$\begin{array}{l|llll} x_{i} & 0 & 1 & 2 & 3 \\ \hline p_{i} & 0.80 & 0.10 & 0.05 & 0.05 \end{array}$$

Mhm. The probability That the random variable is greater than or equal to two Equals the probability that it equals to plus the probability that it equals three plus the probability that it equals four And this equals .05, 1.05 Plus zero Robot, Their vehicles .1 thought, and the expectation echoes the sun of the value of X I times its probability metric, als zero times 00.7 Plus one times .15 plus two points times 0.5 plus three times 30.5 and plus four times 40.5 Hence their sickles, points 15 last 0.1 Plus .15 plus point to Which vehicles .6.

Yeah. The probability that a random variable Is greater than or equal to two. Because the probability is that 8, 8 holes too, Since the random variable can take -2 -101 M2. And so their sickles point to. Mhm And its expectation he calls assam mhm of the value of the outside times is probability. Richie calls -2 times point to plus minus one times point to Plus zero times point to Because one times point to Plus two times point to. And this it goes miners point fel Miners .2 plus .2 plus .4 and The final answer is zero.

Mhm. The probability that the random variable X is greater than equal to two equals the probability that it equals two, and this equals point what? And the expectation of the acts equals the song of the value of X. I times its probability. Richie curls -2 times .1 -1 times point to Plus zero tyrants, .4 Plus one times, point to The last two times .1, which it calls minus point to miners, point to plus point to platform two. And so final answer is zero. Yeah.

Okay. These problems are asking you to read a table of Z values and find whatever probabilities they ask you find this table usually at the end of your textbook or a quick google search will bring it up in google cumulative normal probability table. Okay so for letter A letter A is talking about um values of Z Between negative 2.15 And -1.09. Okay, wants to know what the probability of getting a Z value between those two numbers is. Okay. So we need to find look at our table and find the number of the probabilities for each of these values. So negative 2.15 is .0158. Mhm. And -1.09 is .1379. All right now for each of these problems, you always need to take the larger Z value that the probability from the larger Z value this and subtract it from the smaller z values to 1.1379 minus 0.158 Anytime you have a range of numbers like this, you always take the bigger minus the smaller to get your probability. So 13.79 -1.58. This is 12.21%. The probability of 12.21%. That z value falls between these negative 2.15 and negative 1.09. Alright, let her be same question two different numbers negative 0.93 and 0.55. Okay. Again look on your table, negative .93 is 17.62%. Mhm. And 0.55 is 70.88%. And then you just subtract them 7.88 -17.62 53.26%. And similarly for letter D, we have 0.682, 0468 on my table is 75.17, Yeah, 2.11 is 98.26. So subtract 98.26 -75.17. Mhm. And you get 23.09%.


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