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Basic Question 0 of 4
For x, a normal random variable, which of the following is (are) false?
II. The parameters are the mean and standard deviation.
III. The graph is a bell-shaped curve.
IV. The probability x is equal to a particular value (say, 55) is zero.
I. The parameters are N and p.
II. The parameters are the mean and standard deviation.
III. The graph is a bell-shaped curve.
IV. The probability x is equal to a particular value (say, 55) is zero.
User Contributed Comments 7
| User | Comment |
|---|---|
| standaert | why is anser IV correct? |
| kevin | IV is correct as you can only calculate the probability of x when it falls in a range, such as 56 > x > 54. The probability of x equaling to one exact value is definitely 0. |
| surob | It is because it is continuous distribution |
| bobert | Because in a continuous distribution there are unlimited potential outcomes between the ranges, say -infinity to +infinity. so if you have a value of X = 55 like the example, it would be X/infinity or 55/infinity. This is mathematically impossible though because infinity is not a real number. It would be successively smaller and smaller, but how do you calculate an always decreasing number? Simply put, you cant. 0 would be the limit to which it can go because as infinity increases in the denominator, the probability would get smaller and smaller. As I had said however, infinity is a concept, a word, therefore do not think that x/infinity = 0. Sorry for the long winded explanation, just hope to make it clear. |
| Yurik74 | bobert - mathematician? |
| Dsatti | But its not EQUAL to zero, it tends to zeros as n tends to infinity does it not? So mathematically you can't say it equals zero?! |
| johntan1979 | Prove it, Mr Wiseguy. |
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Learning Outcome Statements
explain the key properties of the normal distribution;
contrast a multivariate distribution and a univariate distribution, and explain the role of correlation in the multivariate normal distribution;
calculate the probability that a normally distributed random variable lies inside a given interval;
CFA® 2024 Level I Curriculum, Volume 1, Module 4.