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Identify the given values as a discrete random variable, continuous random variable, or not a random variable.a. Exact weights of quarters now in circulation in the...

Question

Identify the given values as a discrete random variable, continuous random variable, or not a random variable.a. Exact weights of quarters now in circulation in the United Statesb. Numbers of tosses of quarters required to get headsc. Responses to the survey question "Did you smoke at least one cigarette in the last week?"d. Numbers of spins of roulette wheels required to get the number 7e. Exact foot lengths of humansf. Shoe sizes (such as 8 or $81 / 2$ ) of humans

Identify the given values as a discrete random variable, continuous random variable, or not a random variable. a. Exact weights of quarters now in circulation in the United States b. Numbers of tosses of quarters required to get heads c. Responses to the survey question "Did you smoke at least one cigarette in the last week?" d. Numbers of spins of roulette wheels required to get the number 7 e. Exact foot lengths of humans f. Shoe sizes (such as 8 or $81 / 2$ ) of humans



Answers

Identify the given values as a discrete random variable, continuous random variable, or not a random variable. a. Exact weights of quarters now in circulation in the United States b. Numbers of tosses of quarters required to get heads c. Responses to the survey question "Did you smoke at least one cigarette in the last week?" d. Numbers of spins of roulette wheels required to get the number 7 e. Exact foot lengths of humans f. Shoe sizes (such as 8 or $81 / 2$ ) of humans

All right. So we're flipping a coin twice. First were asked to find the experimental outcomes. And considering that this coin probably has just heads entails to beat you, heads, head spin a tale tailed on our heads or two tails. All right, now we're gonna need to define inappropriate random variable for this. For that, I'm gonna make the random variable X equals the number of heads, Right? Parts e ex Excuse me. Asked us to connect these random variables, your experimental outcomes. So let's do that. So, for H H double heads that corresponds that X equals two for H T. That corresponds to X equals one for T H correspondence. X equals one as well, and for t t that correspond to X equals zero Finally or asked, Is this a continuous variable or discreet variable? And this is a discreet variable. It's very discreet, Yes, And we know that because X can only take a value 01 or two. Only those values you can't be anywhere in between. We can't have half of a head X can equal 0.5 or 1.5 or something like that. No, it has to be zero water, too. So therefore, it's a discreet variable

All right. So for number eight, we're gonna do a problem about tossing a coin and really or die so sample space. We can calculate that by thinking about the possibilities. First of filming a coin there, too, because there is a head and there's a tell and then for really and I there six sides for a dye, which is going to be times six. So there symbol, size of a sample space of 12 to find the probability of getting heads and even number. So within the sample space, we can kind of count out the possibilities. So there's a head. And then there's two heads and four heads in six for those air three possibilities and three divided by 12 is 1/4. Okay, so next is final. Probability of getting heads in a number greater than four. So public of heads and number greater than four is gonna be two possibilities five and six for a grand total of two possibilities provided by 12 which is the sample space. And it'll be 16 Okay, less. One is final probability of getting tails and on number so you can have a tales. One onda number one tails and the number three entails and the number five. So there are three possibilities for ah sample space of 12 which will be 1/4.

So we can see all the probabilities are between zero and one. And also the sum of all The probability is yuko so one. And for me we can see Okay, Like, uh, here is a lie. And here it's a p So the first one's really large. Maybe we just like here. Two euro coin t roll one cool 34 fry 678 So for why you canceled zero is really larger is 00.268 Maybe life here so far, far away. So he doesn't see only this year Like we cannot see. Okay, Eso que so brown. So it's really a large. And for one that a close to 0.5 that is 765 This year that iss one onto we can see that it's someone for three that is eight and four. It's also fried six five. Sorry, that is five is Poland for those lines five and six that is one and true is going to euro True, so you can't see it? That's one That's a rat Screw Infer, sir, Question this crab we want Why is Liszt and Simon in worse? So the probability off why I left and seven. That means work out at most I win. Not like like, not like as more someone that ISS last in seven so that he goes to Ryan Coastal Zero. Well, why you close one class when? Why eak Also true Stray for fry six. You know, so we can see that stress, because who won minus ah, probability when why you cooked with Simon So that Eco's who upon tonight eight on those over b work out at least once. That men's the probability of why it's larger or ecosystem one. And that stress equals who one man us rather work out. It is one manos point as a property of unlike us off the road so you can see that the council points 32

In question 50. We want to defined the random variable X bar in words, so X bar is going to be an average. It's the simple, simple mean in this case, it told us in the problem. The exit's gonna be the number of colors on a national flag. So X bar would be the average number of colors for the mean number of colors because it's X bar. Referring to the sample, we're gonna look at the 39 flags that we looked up, so it's the mean number of colors of 39 national flags.


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