There are a lot of numbers that fall into that category...
Lets call your number x, then 400 < x < 312
That means x can be any number in between 400 and 312. But, x cannot be 400 or 312
x can be a total of 87 numbers which are listed here:
<span>
<span><span>
313,
</span>
<span>
314,
</span>
<span>
315,
</span>
<span>
316,
</span>
<span>
317,
</span>
<span>
318,
</span>
<span>
319,
</span>
<span>
320,
</span>
<span>
321,
</span>
<span>
322,
</span>
<span>
323,
</span>
<span>
324,
</span>
<span>
325,
</span>
<span>
326,
</span>
<span>
327,
</span>
<span>
328,
</span>
<span>
329, </span><span>330,
</span>
<span>
331,
</span>
<span>
332,
</span>
<span>
333,
</span>
<span>
334,
</span>
<span>
335,
</span>
<span>
336,
</span>
<span>
337,
</span>
<span>
338,
</span>
<span>
339,
</span>
<span>
340,
</span>
<span>
341,
</span>
<span>
342,
</span>
<span>
343,
</span>
<span>
344,
</span>
<span>
345,
</span>
<span>
346, </span><span>347,
</span>
<span>
348,
</span>
<span>
349,
</span>
<span>
350,
</span>
<span>
351,
</span>
<span>
352,
</span>
<span>
353,
</span>
<span>
354,
</span>
<span>
355,
</span>
<span>
356,
</span>
<span>
357,
</span>
<span>
358,
</span>
<span>
359,
</span>
<span>
360,
</span>
<span>
361,
</span>
<span>
362,
</span>
<span>
363,
</span>
<span>
364,
</span>
<span>
365, </span><span>366,
</span>
<span>
367,
</span>
<span>
368,
</span>
<span>
369,
</span>
<span>
370,
</span>
<span>
371,
</span>
<span>
372,
</span>
<span>
373,
</span>
<span>
374,
</span>
<span>
375,
</span>
<span>
376,
</span>
<span>
377,
</span>
<span>
378,
</span>
<span>
379, </span><span>380, </span><span>381,
</span>
<span>
382,
</span>
<span>
383,
</span>
<span>
384,
</span>
<span>
385,
</span>
<span>
386,
</span>
<span>
387,
</span>
<span>
388,
</span>
<span>
389,
</span>
<span>
390,
</span>
<span>
391,
</span>
<span>
392,
</span>
<span>
393,
</span>
<span>
394,
</span>
<span>
395,
</span>
<span>
396,
</span>
<span>
397,
</span>
<span>
398, and
</span>
<span>
399.
</span>
</span></span>
Answer:
a) P(X=x) = p× (1-p)^(x-1)
b) P(X=3) = 0.081
c) P(X≤5) = 0.40951
d) Mean of X= 10
e) Var(X)= 90
Step-by-step explanation:
This is a question on geometric distribution.
In geometric distribution, we have two possible outcomes for each trial (success or failure) for independent number of binomials series trial. Also the probability of success is constant for each trial.
This discrete probability distribution is represented by the probability density function: f(x) = p× (1-p)^(x-1)
For a random variable with a geometric distribution, we do not know the number of trials we will have = {1, 2, 3, ...}
We stop the trials when we get a success.
From the question, there are 10 numbers
The probability of success = p = 1/10
For the solutions of the question from (a-e), See attachment below.
f(x) = P(X= x)
Where P(X= x) is the probability of X taking on a value x
