Two professors are applying for grants. Professor Jane has a probability of 0.64 of being funded. Professor Joe has probability
1 answer:
Answer:
14.72% probability that both professors get their grants funded
Step-by-step explanation:
Independent events:
If two events, A and B are independent, the probability of both happening is:
In this question:
Event A: Professor Jane is funded
Event B: Professor Joe is funded.
Professor Jane has a probability of 0.64 of being funded.
This means that
Professor Joe has probability 0.23 of being funded.
This means that
What is the probability that both professors get their grants funded
14.72% probability that both professors get their grants funded
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Well, is the function continuous? yes, is a cubic one, you can graph it if you wish, is continuous all the way, and of course at [ 0, 4] too.
is it differentiable? you can always look at the graph between 0,4 and is a smooth transition line, thus yes, it is differentiable, but let's check anyway,
its derivative has no asymptotes and therefore no "cusps", so yes, is differentiable all around.
is f(0) = f(4), let's check
f(0) = 0+0+0+3, f(0) = 3
f(4) = 64 - 16 - 48 + 3, f(4) = 3
yeap
there must then be a "c" value(s) with a horizontal tangent slope, let's check, is really just the critical points.
is it differentiable? you can always look at the graph between 0,4 and is a smooth transition line, thus yes, it is differentiable, but let's check anyway,
is f(0) = f(4), let's check
f(0) = 0+0+0+3, f(0) = 3
f(4) = 64 - 16 - 48 + 3, f(4) = 3
yeap
there must then be a "c" value(s) with a horizontal tangent slope, let's check, is really just the critical points.