Here Σ i k i means the sum of the k i outcomes. Then the formula for the mean if there are N draws is μ = Σ i k i/ N. For example, from the table, k 1 = 1 and k 5 = 0. Whether or not that guess holds can be checked by looking at Table 16.9 and calculating the mean of the outcome. Before you read any further, ask, “What do you think the average ought to be from the coin flipping exercise?” It is natural to say 0.5, since half the time the outcome will be a head and thus have a value of zero, whereas the remainder of the time the outcome will be a tail and thus have a value of one. The first is the mean (or average) and is a measure of central tendency. We use the data from the table to define and illustrate two statistics that are commonly used in economics discussions. Both the pie chart and the bar diagram are commonly found in spreadsheet programs.Įconomists and statisticians often want to describe data in terms of numbers rather than figures. Alternatively, a pie chart is often used to display this fraction. One possibility is a bar graph in which the fraction of observations of each outcome is easily shown. Even before you start to compute some complicated statistics, having a way to present the data is important. There are many ways to summarize the information contained in a sample of data. Whether a coin comes up heads or tails on any particular flip does not depend on other outcomes. Keep in mind that the realization of the random number in draw i is independent of the realizations of the random numbers in both past and future draws. The choice of 0.5 as the cutoff for heads reflects the fact that we are considering the flips of a fair coin in which each side has the same probability: 0.5. To generate this last column, we adopted a rule: if the random number was less than 0.5, we termed this a “tail” and assigned a 0 to the draw otherwise we termed it a “head” and assigned a 1 to the draw. The third column creates the two events of heads and tails that we normally associate with a coin flip. Those choices are listed in the second column of Table 16.9. In the program we used, the function was called RAND and this generated the choice of a number between zero and one. To generate the data set, we drew 10 random numbers using the spreadsheet program. #VARIANCE OF COIN FLIP FULL#Although you might think it would be easier just to flip a coin, doing this on a spreadsheet gives you a full range of tools embedded in that program. The idea is to simulate the flipping of a two-sided coin. We can also find the standard deviation of ?X?, ?\sigma_X?, which is just the square root of the variance.To start our presentation of descriptive statistics, we construct a data set using a spreadsheet program. Let’s find the variance when ?X? is the number of heads we get when we flip a coin two times, remembering that we already found ?E(X)=1? for this probability distribution. We’ll do that for each value of ?X?, and then add all those results together to get the variance, ?\sigma_X^2?. To find the variance, we’ll take the difference between ?X? and the mean, ?\mu_X?, square that difference, and then multiply the result by the probability of ?X?, called ?P(X)?. We can also find the variance and standard deviation for discrete random variables.
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If you want to go really old school and get teriyaki or tempura, there it is, served with salad and steamed rice (white or brown). There are two dozen small dishes, ranging from barbecue beef ribs to grilled yellowtail collar to Cajun salmon tataki. There are eight salads, mostly made with seafood. In the California style, there’s much more on the menu. It may be theoretically possible - that whole thing about calories expended warming the cold food - but I don’t think it works that well. Deepfried sushi feels a bit like eating ice cream to lose weight. I tend to think of sushi as my go-to cuisine when I need to slim down the old waistline a tad. It is notable that, in the California style, there is a fondness for deepfried rolls and rolls made with cream cheese, and with mayonnaise. They fall apart pretty easily and ingredients are layered on a bit unevenly - not that that makes the Dragon Roll (barbecue eel on top of a California Roll) any less tasty. The rolls are good, but they do seem to be made with some haste. And a Rolling Hills Roll is a Crunchy Roll with avocado and eel on top. Why a California Roll topped with spicy tuna is a Hawaiian Roll is a mystery where’s the pineapple? Top a California Roll with salmon and tempura crunchies, and it becomes a Sunshine Roll. (There are big screens over the sushi bar for those who want to linger.)īut if you want to run a bit amok, there’s the very California section of the menu referred to simply as: “Chef’s Special Rolls.” That’s where you’ll find 22 bits of complex exotica, which in the great tradition often have names that have little to do with what’s in the roll. There are three party trays as well, for those who want to watch the football season get under way at home while nibbling on sushi. For those who can’t make up their minds, there are two sushi samplers, and a sashimi deluxe. There are nine old school hand rolls, and 12 old school cut rolls. You want mackerel (Spanish or otherwise), snapper, yellowtail (including the belly cut), bluefin tuna - it’s all there. The menu lists two dozen fish options for classic nigiri sushi( sushi rice topped with a slice of seafood, held in place with a strip of seaweed). One can, of course, stay wholly conventional at Asaka. I have the same respect for places that offer several dozen exotic sushi rolls, that I do for pizza restaurants that redefine the options (imagine life without barbecue chicken pizza, and you’ll know what I mean.) This may sound like a backhanded compliment, but really, it’s not. I tend to think of restaurants like Asaka, in all the best ways, as a California Japanese restaurant a Los Angeles sushi bar. There are places where you’ll be asked to leave if you request a spicy tuna roll (or anything with spicy tuna for that matter), and where you’ll be chastised for mixing wasabi with your soy sauce - or for even using soy sauce without the permission of the sushi chef. There are Japanese restaurants around town that are doctrinaire in their adherence to the traditional ways of making and serving their food. You can spend a very pleasant afternoon or evening lingering there, watching the shoppers and folks coming from the beach, while sipping on a cold sake and nibbling an exotic roll. But at the branch of Asaka Sushi & Grill in the bustling Riviera Village section of Redondo Beach, the outdoor seating is on a sprawling patio that extends from the restaurant to the street. Though it’s not completely unknown, sushi bars with outdoor seating is a rare bird and of the few (like Katsuya in Brentwood and Kabuki in Old Pasadena), the outdoor option tends to be in a sheltered patio outside the front door. Tarsal coalition is a congenital condition (present since birth) and is often hereditary.įind out all about the common causes, symptoms and treatment options in the Tarsal Coalition section. 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