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ohaa [14]
3 years ago
7

2. A spike train, commonly used to study neural activity, is a sequence of recorded times at which a neuron fires an action pote

ntial (spike). The time in between consecutive spikes is called the interspike interval (ISI). Answer the questions below for an experiment in which the firing rate for a neuron is 10 per second. (a) Let X represent a single interspike interval (ISI) having an exponential distribution. State the distribution of X and give its parameter value(s). (2 points) (b) Give the expected value and variance for an interspike interval (ISI). (4 points) (c) What is the probability that an ISI is less than 0.07 seconds
Mathematics
1 answer:
nika2105 [10]3 years ago
5 0

Answer:

a) X ~ exp ( 10 )

b) E(X) = 0.1 , Var (X) = 0.01

c)  P ( X < 0.07 ) = 0.00698

Step-by-step explanation:

Solution:-

- The spike train, used to study neural activity, the given time in between consecutive spikes (ISI) where the firing rate = 10 neurons per seconds.

- Denote a random variable "X"represent a single interspike interval (ISI) having an exponential distribution.

- Where X follows exponential distribution defined by event rate parameter i.e λ.

                               X ~ Exp ( λ )

- The event rate (λ) is the number of times an event occurs per unit time. Since we are studying a single interspike interval (ISI) - which corresponds to the firing rate. So, event rate (λ) = firing rate = 10 neurons per second. Hence, the distribution is:

                               X ~ Exp ( 10 )

- The expected value E(X) denotes the amount of time in which a single an event occurs; hence, the time taken for a single neuron.

                               E(X) = 1 / λ

                               E(X) = 1 / 10

                               E(X) = 0.1 s per neuron.

- The variance is the variation in the time taken by a single neuron to be emitted. It is defined as:

                               Var (X) = 1 / λ^2

                               Var (X) = 1 / 10^2

                               Var (X) = 0.01 s^2

- The probability that ISI is less than t = 0.07 seconds: P ( X < t = 0.07 s):

- The cumulative distribution function for exponential variate "X" is:

                                P ( X < t ) = 1 - e^(-λ*t)

- Plug the values and the determine:

                                P ( X < 0.07 ) = 1 - e^(-0.1*0.07)

                                                      = 1 - 0.99302

                                                      = 0.00698

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Dafna1 [17]

Answer:

\frac{10}{11}

Step-by-step explanation:

The formula for the trigonometric function sin is:

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The side opposite to the ∠g is x, which is equal to 10

opposite=x      x=10

the hypotenuse of the triangle is z, which is equal to 11

hypotenuse=z    z=11

so the ratio is:

\frac{10}{11}

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8 0
3 years ago
Joe has 37 coins consisting of nickels, dimes, and quarters. There are four more nickels than dimes and two more quarters than n
astraxan [27]

Answer:

  15

Step-by-step explanation:

Let n, d, q represent the numbers of nickels, dimes, and quarters. The problem statement tells us ...

  n +d +q = 37

  n = d +4

  q = n +2

___

Rearranging the second equation gives ...

  d = n -4

Substituting that into the first, we get ...

  n + (n -4) +q = 37

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Rearranging the third original equation gives ...

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Substituting into the equation we just made, we get ...

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Joe has 15 quarters.

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The number of nickels is 2 fewer, so is 13. The number of dimes is 4 fewer than that, so is 9. The total number of coins is 15 + 13 + 9 = 37, as required.

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X+5+2x+3
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aivan3 [116]

Answer:

a. p(orange) = 5/14

b. p(green) = 3/14

c. p(red) = 1/7  

d. p(brown) = 2/7  

e. p(brown or red) = 3/7

Step-by-step explanation:

1. You have a 14 pencils. Two pencils are red, 5 pencils are orange, 3 pencils are green and 4 pencils are brown.

p(color) = (number of pencils of that color)/(total number of pencils)

p(color) = (number of pencils of that color)/14

a. If a pencil is picked at random, what is the probability that the pencil

will be orange?

p(orange) = 5/14

b. If a pencil is picked at random, what is the probability that the pencil

will be green?

p(green) = 3/14

c. If a pencil is picked at random, what is the probability that the pencil will be red?

p(red) = 2/14 = 1/7

d. If a pencil is picked at random, what is the probability that the pencil

will be brown?

p(brown) = 4/14 = 2/7

e. If a pencil is picked at random, what is the probability that the pencil

will be brown or red?

brown: 4

red: 2

brown or red: 4 + 2

p(brown or red) = 6/14 = 3/7

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3 years ago
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Answer:

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Continue to split the group that has the fake coin into 3 groups, each group has 1 coin. Now apply the same procedure and we can identify the fake coin.

Total of scale usage is 2

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Step 2: you narrow down to group of \frac{3^{n-1}}{3} = 3^{n-2} coins

Step 3: you narrow down to group of \frac{3^{n-2}}{3} = 3^{n-3} coins

...

Step n: Step 1: you narrow down to group of 3^{n-n} = 3^0 = 1coin

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