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Matlab, 24 18 bytes

char(floor(26*rand^2+65))

it looks like using floor(x) isn't necessary as char also takes non-integer inputs

char(25*rand^2+65)

not using ['' x] instead of char(x) so I won't get warning: implicit conversion from numeric to char for "purer" output.

rand yields a uniformly distributed random number in the interval (0,1) but rand^2 isn't uniformy distributed anymore, the probability density function follows , see here.

with (b-a)*rand+a one can shift the interval of the distribution from (0,1) to (a,b), this also works with rand^2.

because i use floor i need to stretch the interval to (65,91) so i don't lose "Z"

It might no be the shortest answer but i like the approach with using a uniform random distribution to get a non-uniform random distribution.

Below is the count for each generated numbers after 20000 iterations (using my first version of my answer).

Matlab, 24 18 bytes

char(floor(26*rand^2+65))

it looks like using floor(x) isn't necessary as char also takes non-integer inputs

char(25*rand^2+65)

not using ['' x] instead of char(x) so I won't get warning: implicit conversion from numeric to char for "purer" output.

rand yields a uniformly distributed random number in the interval (0,1) but rand^2 isn't uniformy distributed anymore, the probability density function follows , see here.

with (b-a)*rand+a one can shift the interval of the distribution from (0,1) to (a,b), this also works with rand^2.

because i use floor i need to stretch the interval to (65,91) so i don't lose "Z"

It might no be the shortest answer but i like the approach with using a uniform random distribution to get a non-uniform random distribution.

Below is the count for each generated numbers after 20000 iterations (using my first version of my answer).

Matlab, 24 18 bytes

char(floor(26*rand^2+65))

it looks like using floor(x) isn't necessary as char also takes non-integer inputs

char(25*rand^2+65)

not using ['' x] instead of char(x) so I won't get warning: implicit conversion from numeric to char for "purer" output.

rand yiedls a uniformly distributed random number in the interval (0,1) but rand^2 isn't uniformy distributed anymore, the probability density function follows , see here.

with (b-a)*rand+a one can shift the interval of the distribution from (0,1) to (a,b), this also works with rand^2.

because i use floor i need to strech the interval to (65,91) so i don't lose "Z"

It might no be the shortest answer but i like the approach with using a uniform random distribution to get a non-uniform random distribution.

Below is the count for each generated numbers after 20000 iterations (using my first version of my answer).

Matlab, 24 18 bytes

char(floor(26*rand^2+65))

it looks like using floor(x) isn't necessary as char also takes non-integer inputs

char(25*rand^2+65)

not using ['' x] instead of char(x) so I won't get warning: implicit conversion from numeric to char for "purer" output.

rand yields a uniformly distributed random number in the interval (0,1) but rand^2 isn't uniformy distributed anymore, the probability density function follows , see here.

with (b-a)*rand+a one can shift the interval of the distribution from (0,1) to (a,b), this also works with rand^2.

because i use floor i need to stretch the interval to (65,91) so i don't lose "Z"

It might no be the shortest answer but i like the approach with using a uniform random distribution to get a non-uniform random distribution.

Below is the count for each generated numbers after 20000 iterations (using my first version of my answer).

Matlab, 24 17 bytes

char(floor(26*rand^2+65))

it looks like using floor(x) isn't necessary as char also takes non-integer inputs

char(25*rand^2+65)

not using ['' x] instead of char(x) so I won't get warning: implicit conversion from numeric to char for "purer" output.

rand yiedls a uniformly distributed random number in the interval (0,1) but rand^2 isn't uniformy distributed anymore, the probability density function follows , see here.

with (b-a)*rand+a one can shift the interval of the distribution from (0,1) to (a,b), this also works with rand^2.

because i use floor i need to strech the interval to (65,91) so i don't lose "Z"

It might no be the shortest answer but i like the approach with using a uniform random distribution to get a non-uniform random distribution.

Below is the count for each generated numbers after 20000 iterations (using my first version of my answer).

Matlab, 24 18 bytes

char(floor(26*rand^2+65))

it looks like using floor(x) isn't necessary as char also takes non-integer inputs

char(25*rand^2+65)

not using ['' x] instead of char(x) so I won't get warning: implicit conversion from numeric to char for "purer" output.

rand yiedls a uniformly distributed random number in the interval (0,1) but rand^2 isn't uniformy distributed anymore, the probability density function follows , see here.

with (b-a)*rand+a one can shift the interval of the distribution from (0,1) to (a,b), this also works with rand^2.

because i use floor i need to strech the interval to (65,91) so i don't lose "Z"

It might no be the shortest answer but i like the approach with using a uniform random distribution to get a non-uniform random distribution.

Below is the count for each generated numbers after 20000 iterations (using my first version of my answer).