c. Which of the fallowing are valid statistical models
a) R{N(θ,1)} θ>10
b) (θ,inf) {t->e^ (θ-t) 1(t> θ) } θ>0
c)([0,inf], {N(u,σ^2})u> σ^2
d)([0,inf]), {x->e^ θx 1>(x>0) θ >0}
To determine which of the following options are valid statistical models, we need to understand the notation and conditions specified for each option.
a) R{N(θ,1)} θ>10
This option represents a random variable 'R' that follows a normal distribution with mean θ and standard deviation 1. However, it is only valid for values of θ greater than 10.
b) (θ,inf) {t->e^ (θ-t) 1(t> θ) } θ>0
This option represents a random variable 't' that follows an exponential distribution where the rate parameter is defined as e^(θ-t) only when t is greater than θ. This option is valid for positive values of θ.
c) ([0,inf], {N(u,σ^2})u> σ^2
This option represents a random variable 'u' that follows a normal distribution with mean u and variance σ^2. It is valid for values of u greater than σ^2. The notation [0, inf] represents the range of possible values for 'u'.
d) ([0,inf]), {x->e^ θx 1>(x>0) θ >0}
This option represents a random variable 'x' that follows an exponential distribution with rate parameter θ, but only when x is greater than 0. It is valid for positive values of θ.
Based on the given information, all options (a), (b), (c), and (d) are valid statistical models, given the specified conditions for each option.