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# Q2
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# Q2a
# Physicist A
m.A  = 900
sd.A = 20

# Physicits B
m.B  = 800
sd.B = 80

# Model & data
sd.X = 40
x    = 850
n=length(x)
xbar=mean(x)

tau2.a=1/(1/sd.A^2 + n/sd.X^2)
mu.a=( (1/sd.A^2)*m.A +  n/sd.X^2*xbar )/ (1/sd.A^2 + n/sd.X^2 )

# Posterior Physicist B
tau2.b=1/(1/sd.B^2 + n/sd.X^2)
mu.b=( (1/sd.B^2)*m.B +  n/sd.X^2*xbar )/ (1/sd.B^2 + n/sd.X^2 )

#Answers 2a
#a1) 
pnorm(800,m.A,sd.A)
#a2) 
pnorm(800,mu.a,sqrt(tau2.a))
#a3) 
pnorm(800,m.B,sd.B)
#a4) 
pnorm(800,mu.b,sqrt(tau2.b))

#Q2b
# Physicist A
m.A  = 900
sd.A = 20

# Physicits B
m.B  = 800
sd.B = 80

# Model & data
sd.X = 40
x    = c(850,850)
n=length(x)
xbar=mean(x)

# Posterior Physicist A
tau2.a=1/(1/sd.A^2 + n/sd.X^2)
mu.a=( (1/sd.A^2)*m.A +  n/sd.X^2*xbar )/ (1/sd.A^2 + n/sd.X^2 )

# Posterior Physicist B
tau2.b=1/(1/sd.B^2 + n/sd.X^2)
mu.b=( (1/sd.B^2)*m.B +  n/sd.X^2*xbar )/ (1/sd.B^2 + n/sd.X^2 )

#b1
pnorm(800,mu.a,sqrt(tau2.a))
#b2
pnorm(800,mu.b,sqrt(tau2.b))