Evaluate StartFraction n exclamation mark Over left parenthesis n minus x right parenthesis exclamation mark x exclamation mark EndFraction p Superscript x Baseline times left parenthesis 1 minus p right parenthesis Superscript n minus xn!(n−x)!x!px•(1−p)n−x for nequals=1818, pequals=one fifth15, xequals=22. The answer is ?
Solution
Given that ,
Using binomial probability formula ,
P(X = x) = (n C x) * px * (1 - p)n - x
P(X = 2) = (18 C 2) * 0.22 * (0.8)16
= 0.1723
Probability = 0.1723
Evaluate StartFraction n exclamation mark Over left parenthesis n minus x right parenthesis exclamation mark x...
Use the equation m Subscript PQ Baseline equals StartFraction f left parenthesis x 1 plus h right parenthesis minus f left parenthesis x 1 right parenthesis Over h EndFraction mPQ= fx1+h−fx1 h to calculate the slope of a line tangent to the curve of the function y equals f left parenthesis x right parenthesis equals 2 x squared y=f(x)=2x2 at the point Upper P left parenthesis x 1 comma y 1 right parenthesis equals Upper P left parenthesis 3 comma...
Let
z equals f left parenthesis x comma y right parenthesis
commaz=f(x,y) ,
where
x equals u squared plus v squared and y equals StartFraction u
Over v EndFractionx=u2+v2 and y=uv.
Find
StartFraction partial derivative z Over partial derivative u
EndFraction and StartFraction partial derivative z Over partial
derivative v EndFraction∂z∂u and ∂z∂v
at
left parenthesis u comma v right parenthesis equals left
parenthesis negative 6 comma negative 6 right
parenthesis(u,v)=(−6,−6)
,
given that :
f Subscript x Baseline left parenthesis negative 6 comma...
To construct a confidence interval for the difference between two population means mu 1 minus mu 2, use the formula shown below when both population standard deviations are known, and either both populations are normally distributed or both n 1 greater than or equals 30 and n 2 greater than or equals 30. Also, the samples must be randomly selected and independent. left parenthesis x overbar 1 minus x overbar 2 right parenthesis minus z Subscript c Baseline StartRoot StartFraction...
Evaluate the following formula for ModifyingAbove p with caret 1 equals0.5 , ModifyingAbove p with caret 2 equals0.8 , p 1 minusp 2equals 0, p overbar equals0.835496 , q overbar equals0.273634 , n 1 equals60 , and n 2 equals64 . z equals StartFraction left parenthesis ModifyingAbove p with caret 1 minus ModifyingAbove p with caret 2 right parenthesis minus left parenthesis p 1 minus p 2 right parenthesis Over StartRoot StartFraction p overbar times q overbar Over n 1...
1. Suppose $26002600 is invested annually into an annuity that earns 55% interest. If P dollars are invested annually at an interest rate of r, the value of the annuity after n years is given by the following equation. Upper W equals Upper P left bracket StartFraction left parenthesis 1 plus r right parenthesis Superscript n Baseline minus 1 Over r EndFraction right bracketW=P(1+r)n−1r How much is the annuity worth after 5 years? 2. Suppose that $90,000 is invested at...
Use f prime left parenthesis x right parenthesis equals ModifyingBelow lim With h right arrow 0 StartFraction f left parenthesis x plus h right parenthesis minus f left parenthesis x right parenthesis Over h EndFractionf′(x)=limh→0 f(x+h)−f(x) h to find the derivative at x for the given function. s left parenthesis x right parenthesis equals 2 x plus 6s(x)=2x+6 s prime left parenthesis x right parenthesiss′(x)equals=nothing
Given y equals f(u) and u equals g(x), find StartFraction dy Over dx EndFraction equals f prime left parenthesis g left parenthesis x right parenthesis for the following functions y equals sin, Equals 7x plus 4
Determine ModifyingBelow lim With x right arrow c Superscript plusf(x), ModifyingBelow lim With x right arrow c Superscript minusf(x), and ModifyingBelow lim With x right arrow cf(x), if it exists. cequals3, f(x)equals left brace Start 2 By 2 Matrix 1st Row 1st Column 4 minus x 2nd Column x less than 3 2nd Row 1st Column StartFraction x Over 3 EndFraction plus 1 2nd Column x greater than 3 EndMatrix ModifyingBelow lim With x right arrow c Superscript plusf(x)equals nothing...
The following function is probability mass function. f left-parenthesis x right-parenthesis equals StartFraction 6x plus 2Over 70EndFraction comma x equals 0 comma 1 comma 2 comma 3 comma 4 Determine the mean, μ, and variance, σ2, of the random variable. Round your answers to two decimal places (e.g. 98.76). μ = σ2 =
Determine ModifyingBelow lim With x right arrow c Superscript pluslimx→c+f(x), ModifyingBelow lim With x right arrow c Superscript minuslimx→c−f(x), and ModifyingBelow lim With x right arrow climx→cf(x), if it exists. cequals=22, f(x)equals= left brace Start 2 By 2 Matrix 1st Row 1st Column 3 minus x 2nd Column x less than 2 2nd Row 1st Column StartFraction x Over 2 EndFraction plus 1 2nd Column x greater than 2 EndMatrix 3−x x<2 x2+1 x>2