Disk storage channel. Binary data storage with a thin-film disk can be approximated by an input-dependent additive white Gaussia
n noise channel where the noise n has a variance dependent on the transmitted (stored) input. The noise has the following input dependent density: 2 2ơ 2To2 2ơ 2Ta2 0 and σ-31ơ1. The channel inputs are equally-likely. a. For either input, the output can take on any real value. On the same graph, plot the two possible output probability density functions (pdf's). i.e. Plot the output pdf for 0 and the output pdf for x -1. Indicate (qualitatively) the decision regions on your graph. 2 72 2πσ 2 2πσ 2 0
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Answer:
probability that all of the sprinklers will operate correctly in a fire: 0.0282
Step-by-step explanation:
In order to solve this question we will use Binomial probability distribution because:
- In the question it is given that the sprinklers activate correctly or not independently.
- The number of outcomes are two i.e. sprinklers activate correctly or not.
A binomial distribution is a probability of a success or failures outcomes in an repeated multiple or n times.
Number of outcomes of this distributions are two.
The formula is:
b(x; n, P) =
b = binomial probability also represented as P(X=x)
x =no of successes
P = probability of a success on a single trial
n = no of trials
is calculated as:
= n! / x!(n – x)!
= 10! / 10!(10-10)!
= 1
According to given question:
probability of success i.e. p = 0.7 i.e. probability of a sprinkler to activate correctly.
number of trials i.e. n = 10 as number of sprinklers are 10
To find: probability that all of the sprinklers will operate correctly in a fire
X = 10 because we have to find the probability that "all" of the sprinklers will operate correctly and there are 10 sprinklers so all 10 of them
So putting these into the formula:
P(X=x) =
= C₁₀,₁₀ * 0.7¹⁰ * (1-0.7)¹⁰⁻¹⁰
= 1 * 0.0282 * (0.3) ⁰
= 1 * 0.0282 * 1
P(X=x) = 0.0282